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IdentifierTypeTitle1838194Postgraduate Thesis'Proof Complexity: A Tableau PerspectiveUnitDeposit dateYearAuthorSupervisors infoOriginal Title LanguagesTranslated titleSummaryMain subject categoryOther subject categoriesKeywordsIndexNumber of index pagesContains imagesNumber of referencesNumber of pagesNotes> , Library of the School of Science
201708302017Papamakarios Theodoros5 ,
, EnglishThe method of semantic tableaux (or simply tableaux) is arguably
one of the most elegant proof systems. Unfortunately, it hasn t received
much attention in the proof complexity literature, mainly due to early
negative results, concerning the complexity of cutfree tableaux. We bring tableaux to the fore, introducing the
measures of tableau depth and width. Equipped with these, we show in
an elegant, uniform way several known results spanning proof complexity,
from a tableau viewpoint.Science>proof complexity, tableaux, width, depth, consistency propertyfalse0true38591332104ALearning Poisson Binomial Distributions with Differential PrivacyY , Library of the School of Science
20170301Giannakopoulos Agamemnon@ , , ...
, , ...
, , ...This thesis tries to leverage two major research areas. The first area concerns the Distribution Learning area and the second the Differential Privacy. More specific, given a highly efficient algorithm which learns with accuracy a Poisson Binomial distribution we try to study its Differential Privacy property. We show that if the algorithm is close to a (n,k)Binomial form the algorithm is differential private. If the PBD is close to a kSparse form the algorithm's privacy depends on PBD cardinalityMathematics@Learning, Poisson, Binomial, Distribution, Differential, Privacy51671708336/Geometric Proximity Problems in High Dimensions
20170706Avarikioti Georgiap . , , & , 8Geometric proximity problems is a class of problems in computational geometry that involve estimation of distances between geometric objects.
In this work, we focus on two specific problems of this class, the computation of rnets and the near neighbor decision problem on high dimensional spaces under the Euclidean distance, both of which are powerful tools in computational and metric geometry.
Specifically, we present a new randomized algorithm which efficiently computes high dimensional approximate rnets with respect to Euclidean distance. For any fixed >0, the approximation factor is 1+ and the complexity is polynomial in the dimension and subquadratic in the number of points; the algorithm succeeds with high probability. We improve upon the best previously known (LSHbased) construction of Eppstein et al. in terms of complexity, by reducing the dependence on , provided that is sufficiently small. Moreover, our method does not require LSH but follows Valiant's approach in designing a sequence of reductions of our problem to other problems in different spaces, under Euclidean distance or inner product, for which rnets are computed efficiently and the error can be controlled. Our result immediately implies efficient solutions to a number of geometric problems in high dimension, such as finding the (1+)approximate kth nearest neighbor distance in time subquadratic in the size of the input.
Additionally, we propose a new and simple data structure for the capproximate near neighbor decision problem in highdimensional spaces using linear space and sublinear query time for any c>1: given an LSH family of functions for some metric space, we randomly project points to vertices of the Hamming cube in dimension d"log n, where n is the number of input points. The projected space contains strings which serve as keys for buckets containing the input points. The query algorithm simply projects the query point, then examines points which are assigned to the same or nearby vertices on the Hamming cube. We ana< lyze in detail the query time for some standard LSH families.$Algorithms and Theory of Computationcomputational geometry, metric geometry, general dimension, approximation algorithm, rnets, Locality Sensitive Hashing, Near Neighbor, high dimension, linear storage, sublinear query, random projection234681672490%Polytope Membership in High Dimension
20170619Anagnostopoulos Evangelos , , ,
, , ,
, , , Polytopes in optimization and sampling problems are usually given by implicit rep
resentations through oracles. The most basic oracle is the polytope membership ora
cle which can identify whether a query point q lies inside P or not and is often used
as the basis for more complex oracles, such as the separation oracle or the bound
ary oracle. In this work we aim to design, implement and analyse algorithms for
approximating the membership oracle in polytopes given as the intersection of half
spaces in high dimension, by trading exactness for efficiency. Previous approaches
were based on classic polytope approximation techniques which, however, have
complexity that scales exponentially in the dimension and are, thus, intractable in
high dimension. We establish a straightforward reduction from approximate poly
tope membership to approximate nearest neighbor search among points and obtain
complexity bounds polynomial in the dimension, by exploiting recent progress in
the complexity of nearest neighbor search. We then employ this new membership
oracle to obtain a solution for the boundary oracle in high dimension. Lastly, we
evaluate our algorithms experimentally and report results.wpolytope,high dimension,membership oracle,boundary oracle,approximate polytope membership,approximate polytope boundary11917102776Transfer kmeans: a new supervised clustering approach
20170711Teloni Pelagia\ , , , Supervised and unsupervised learning are two fundamental learning schemes
whose difference lies in the presence and absence of a supervisor
(i.e. entity which provides examples) respectively. On the other hand,
transfer learning aims at improving the learning of a task by using auxiliary knowledge.
The goal of this thesis was to investigate how the two fundamental paradigms,
supervised and unsupervised learning, can collaborate in the setting of transfer learning.
As a result, we developed transfer$K$means, a transfer learning variant
of the popular $K$means heuristic.
The proposed method enhances the unsupervised nature of $K$means, using
supervision from a different but related context as a seeding technique,
in order to improve the heuristic's performance towards more meaningful
results. We provide approximation guarantees based on the nature of
the input and we experimentally validate the benefits of the proposed
method using documents as a realworld example.gclustering, transfer learning, domain adaptation, density ratio estimation, natural language processing81731326064(OPINION DYNAMICS WITH LOCAL INTERACTIONS
201612142016 SKOULAKIS EFSTRATIOSPANTELEIMON# . ,During the last century many researchers investigated the way individuals form their
opinions. The rapid growth of social networks in the recent years (Facebook,Twitter e.t.c)
has further intensified this interest. To this day, a lot of models, on how our opinions
evolve, have been proposed. In the huge majority of these models, each agent has to learn
a large amount of opinions of other agents in order to update her opinion. In this thesis,
we investigate the well studied HegelsmannKrause and FreidkinJohson Model, under
the constraint that each agent can learn a small amount of opinions of other agents. We
propose three vatiations of these models, namely Network HegelsmannKrause, Random
HegelsmannKrause and Limited Information FriedkinJohson Model and we investigate
their convergence properties.HegelsmannKrause Model273521826971NonStrict Pattern Matching and Delimited Control
20171110Barbagiannis Petros} ,
It has been long known that continuations and evaluation strategies are two intimately related concepts of functional programming languages. In one of the earliest results, continuationpassing style (CPS) was introduced as a means to decouple the evaluation order of a language from the evaluation order of its interpreter. Since then, this style of programming has been proved extremely useful in areas ranging from compiler implementation to denotational semantics.
Since the introduction of CPS, a wide variety of control operators have been developed. Delimited control operators, in particular, are a powerful mechanism of functional programming languages that generalize traditional firstclass control operators, such as \texttt{call/cc}, and provide the means to abstract control. One notable application of delimited control operators is the construction of a novel abstract machine for the callbyneed $\lambda$calculus that simulates storebased effects with delimited continuations.
Pattern matching on algebraic data types is an essential feature of functional programming languages. However, pattern matching is often thought to be syntactic sugar that can be merely represented by a proper encoding. In this thesis we study the operational characteristics of nonstrict pattern matching. We also explore the semantics of control operators, as well as some of their applications. Finally, we seek to examine the connection between implementing a nonstrict pattern matching evaluator and delimited continuations.\functional programming languages, delimited continuations, pattern matching, lazy evaluation29741325627>Quantum Complexity, Relativized Worlds, and Oracle Separations
20161129 ~
The complexity class QMA, defined by Watrous, in 2000, is the quantum
analogue of MA, defined by Babai, in 1985, which, in turn, is a generalization
of the class NP. The class MA generalizes the class NP in the sense that the
verification procedure of the purported proof, put forth by the prover, is
carried out by a probabilistic machine, rather than a deterministic one as
the definition of the class NP demands.
In 2014, Grilo, Kerenidis, and Sikora, proved that the quantum proof, in
the setting of QMA, may always be replaced by, an appropriately defined,
quantum subset state without any conceptual loss. T< hat is, QMA " SQMA.
Grilo et al., named their new class SQMA, for subsetstate quantum MerlinArthur.
Thus, one could write that SQMA = QMA, as the inclusion SQMA "
QMA holds trivially.
After this result, by Grilo, Kerenidis, and Sikora, Fefferman and Kimmel, in
2015, used this new characterization of QMA, and further proved that there
exists some quantum oracle A similar to that Aaronson and Kuperberg
introduced, and used, in 2006, to show that QMAA
1 6" QCMAA which is
such that QMAA = SQMAA 6" QCMAA. Here, QCMA is that version of QMA,
defined by Aharonov, and Naveh, in 2002, in which the purported proof
is purelyclassical, that is, a bitstring, and QMA1 is the perfect completeness
version of QMA. In their separation, Fefferman and Kimmel introduced, and
used, an interesting template to obtain oracle separations against the class
QCMA.
Drawing upon this recent result, by Fefferman and Kimmel, we prove that
there exists some quantum oracle A, such that SQMAA
1 6" QCMAA. We
note that the class SQMA1 is the perfect completeness version of the class
SQMA. In our proof, we used the template of Fefferman and Kimmel, a
modified version of their basic quantum oracle construction, as well as
the basic decision problem, that they themselves used for their separation.
Note that our result implies that of Fefferman and Kimmel, as the inclusion
xiii
SQMA1 " SQMA holds.
After we state and prove our result, we take a detour to explore a bit the
world of oracle separations, both in the classical and the quantum setting.
That is, we explore some results, and their underlying methods, about
classical and quantum oracles being employed for proving separations
about classical, or quantum, complexity classes. Hence, we investigate
some gems pertaining to the, not few at all, nor uninteresting, privileged
relativized worlds.
Finally, we return, to the research setting, to approach the open question
of whether there exists some classical, or quantum, oracle A, such that
QMAA
1 6" SQMAA
1
, or not. We record our efforts, and some of our first ideas,
thus far."Quantum computational complexity theory, computational complexity theory, relativized worlds, oracle separations, oracles, QMA, QCMA, SQMA, SQMA1, quantum states, quantum subsetstates, quantum proofs, veri fication procedures, verification protocols, diagonalization, and query complexity1061531325895EParameterized Algorithms and Matroids: the use of representative sets
20161209Petropanagiotaki Maria , , ....
,
, , ....J : GreekLet $M = (E, I)$ be a matroid and let $\mathcal{S} = {S_1, ... , S_t}$ be a family of subsets of $E$ of size $p$. A subfamily of $\mathcal{S}$ is said to be $q$representative for $\mathcal{S}$ if some independent set in S can be extended to a larger independent set by $q$ new elements, then there is a set in subfamily that can be extended by the same $q$ elements. By the Two Families Theorem of Bollobs and its algebraic version by Lovsz, there is a $q$representative family with at most sets.
In this paper, we give two algorithms computing representative families. The first algorithm is about linear matroids and it turns Lovsz s proof into an algorithm constructing a $q$representative family in time bounded by a polynomial in $\binom{p+q}{p}$, $t$ and the time required for field operations. The second one is
about uniform matroids and computes a representative family in time $\mathcal{O}((1x)^{q} 2^{o(p+q)} t logn)$.
We demonstrate how the efficient construction of representative families can be a powerful tool for designing parameterized algorithms for the following problems: !MATROID INTERSECTION, LONG DIRECTED CYCLE and kPATH.lrepresentative sets, parameterized algorithms, matroids, !MATROID INTERSECTION, LONG DIRECTED CYCLE, kPATH375723005051ChangeAverse Nash Equilibria in Congestion Games
20171127Mantis Andreas1 , , , DWe introduce a new model in Congestion Games, where the players choose their strategy
according to the new cost they incur, as well as the dierence betwee< n their current state
and the new state they are considering. The latter part of the decisionmaking process is
based on the assumption that players who are considering a signicant change are less prone to take it, than they do on a similar choice. This model has analogies with approximate equilibria. We can easily see that this new model provides a richer set of equilibria than approximate equilibria. Christodoulou et al. prove that as far as Linear Congestion Games are concerned, we have good bounds on the Price of Anarchy. We prove that similar results are true in our case. We also prove that players do actually converge on such an equilibrium and relatively quickly.ACongestion Games, Nash equilibrium, Price of Anarchy, Convergence432244321Online Facility Location with Switching Costs
20171118Zakynthinou Lydia , . , ,
, , ,
, . , , Online decision making is a large research area whose literature includes many different aspects and approaches. The problems it studies are based on the following setting. There is a decisionmaker who has to make a decision iteratively with no knowledge of the future and receive the cost of their decision in each round. The goal is to perform well over time. Depending on the definition of what consists of a good performance, that is the benchmark to which we compare our algorithm s total cost, and on the assumptions made, different kinds of problems occur. A particularly interesting benchmark which captures many real life problems where the environment changes over time, is a solution which balances the tradeoff between the optimal costs in each round and its stability. Online learning and competitive analysis are two frameworks which study problems in this setting. In this thesis we will discuss the differences between these two frameworks, the efforts to unify them and finally we will demonstrate how such a unifying approach can give a good approximation algorithm for the online facility location problem with switching costs, which falls into this general setting.Oonline learning, online convex optimization, facility location, switching costs39762285461)A journey in NonCommutative Cryptography
20171122Partalidou Eleni4 , , , , MM KIn this thesis we are going to start by mentioning a few basic concepts of Noncommutative cryptography
and underline the importance of cryptography from the very early stages of life. Noncommutative
cryptography is defined by the usage of algebraic structures, that are noncommutative, in order to build
systems and methods. As a next step in this journey we will talk about the relationship between computer
science and mathematics in terms of decision problems and of course how they relate. Moreover, we will
present a few groups that could be used as platforms for building safe systems. Later on we shall talk
about a very important scheme and how it is constructed and of course how we can attack it. We will
determine the level of security and the attacks that were more efficient. To sum up, in this thesis we will
present the road so far on the matter and underline a few important points.6protocol, group, attack, noncommutative, cryptography22442285490(Online Shortest Path with Switching Cost
20171123Tziotis Isidorosg , , ., MA typical online problem proceeds in rounds, where in each round an online algorithm is given a request and needs to serve it. We will focus on a specific class of online problems known as Smooth Online Convex Optimization (SOCO) problems. Two mature research fields that study such problems are competitive analysis and online learning. We will dive into their interrelationship and we will explain how we can benefit by introducing regularization, a standard technique from online learning in the framework of competitive analysis. Subsequently, we will turn our attention towards a rounding technique introduced over the last couple of years, called exponential clocks. Finally, we will define a new problem in the class SOCO, namely Online Shortest Path with Switching Cost. Using the toolbox provided by the literature we will obtain an online fractional solution sacrificing a logarithmic factor. We will wrap up presenting a new online rounding algorithm using exponential clocks which will derive a O(logmlog n)approximation for the Online Shortest Path with Switching Cost problem.dOnline Convex Optimization, Smooth Optimization, Online Learning, Shortest Paths, Exponential Clocks32542098333Coercion Resistant evoting.
20171104Kalogeropoulos Panagiotis , , , .
, , ,
, , , .0 NSecurity and privacy of the vote in most evoting protocols are based on the inability of the adversary to break the cryptographic tools that are in use. Since the computational power of the adversary is constantly increasing and the storage of every public information for future use is of negligible cost, what is going to happen in a few years when the cryptographic tools break? The current thesis studies evoting protocols that offer " Everlasting Privacy" and Coercion Resistance". Such properties secure vote privacy against adversaries with infinite computational power and time. They also enable the voter to avoid coercion< . Two voting protocols satisfying these properties, are presented along with the cryptographic tools they implement. In the epilogue, we present our attempt for a third evoting protocol with similar properties.2Everlasting Privacy, coercion resistance, evoting328922286251PTRIANGULATION PROBLEMS ON GEOMETRIC GRAPHS  SAMPLING OVER CONVEX TRIANGULATIONSAngelopoulos Alexandros , ...
, ...
, ...GA geometric graph is a set of points V on the plane and a set of straight line segments E with endpoints in V, potentially and instinctively associated with the abstract G(V,E). When studying its thickness, i.e. partitioning its edges into crossingfree subsets (an NPhard optimization problem), the problem of triangulation existence as a crossingfree subset T of the edges naturally occurs, as a triangulation of V is the largest such possible set that may be defined on V. In this Thesis, we examine a family of triangulation existence problems and classify them with respect to their complexity, both for their decision and their counting versions. The general case decision problem is the only one appearing in bibliography (Lloyd, 1977, NPhard), while we deal with the convex case restriction and an "intermediate" polygon triangulation existence problem, fixing a new 2 by 2 table of results. In the final chapter, we modify our framework in order to build an exact uniform sampling and optimal coding algorithm for convex triangulations, which outperforms any known algorithm to date.igeometric graph, triangulation existence, complexity, counting complexity, convex triangulations sampling42552216203Algorithms in Group Theory
20171115Pilichos Christos? , , ,
, , ,
, , , %A modern branch of Mathematics is NonCommutative Cryptography, which is based on the algorithmic hardness of solving some Group Theory based problems. Since 1911, Max Dehn announced that a part of his interest were the word, conjugacy and groupisomorphism problems. The former two accompanied with the analysis problem consist the fundamental problems on which all the protocols of the current Thesis are based on. The tour in the world of NonCommutative Cryptography begins from the protocols of WagnerMagyarik (using free groups) and GarzonZalcstein (using Grigorchyk's groups) and via AnshelAnshelGoldfeld and KoLee et al. (both using braid groups) is over at protocols of ShpilrainUshakov (using Thompson's group F), Stickel anf Kurt. Cryptanalysis and the tries of making the above cryptosystems more secure creates some interesting byproducts (like a protocol based on circuits, dynamic version of Stickel's protoocol, using monoids in WagnerMagyarik protocol, the generalised version of AnshelAnshelGoldfeld and KoLee et al. protocols, etc).7algorithms, cryptography, group theory, noncommutative751521325624PHigh dimensional Approximate rnets with emphasis on vectors on a unit hypercubeKavouras Loukas . , , ,
, , ,
, , , English, GreekThe construction of $r$nets offers a powerful tool in computational and metric geometry.
We focus on highdimensional spaces and
present a new randomized algorithm which efficiently computes approximate $r$nets with respect to Euclidean distance.
For any fixed $\epsilon>0$,
the approximation factor is $1+\epsilon$ and the complexity is polynomial in the dimension and subquadratic in the number of points. The algorithm succeeds with high probability. More specifically,
the best previously known LSHbased construction of Eppstein et al.\ \cite{EHS15} is improved in terms of complexity by reducing the dependence on $\epsilon$,
provided that $\epsilon$ is sufficiently small.
Our method does not require LSH but, instead, follows Valiant's \cite{Val15} approach in designing a sequence of reductions of our problem to other problems in different spaces, under Euclidean distance or inner product, for which $r$nets are computed efficiently and the error can be controlled.
Our result immediately implies efficient solutions to a number of geometric problems in high dimension, such as finding the $(1+\epsilon)$approximate $k$th nearest neighbor distance in time subquadratic in the size of the input.%approximation, rnets, high dimension141956163Federated Consensus Protocols
20171003Myrto Galenianouh , , , nThis dissertation studies consensus protocols and specifically Raft and the Stellar Consensus protocol. We first define the execution model under which we study the protocols as well as the notion of a robust transaction ledger that we want the protocols to maintain and its properties. We proceed by presenting Raft as concrete algorithm and we prove that indeed Raft maintains a robust transaction ledger. We then move to the Stellar Consensus protocol and analyse federated voting, Stellar s mean to reach consensus. Subsequently, we present the two protocols that constitute the Stellar Consensus protocol, the Nomination and Ballot protocol, as concrete algorithms and further explore their properties. Finally, we show that the Ballot protocol has both
persistence and liveness, the two necessary properties a protocol need to have to maintain a robust transaction ledger.Technology  Computer science9consensus, consensus protocol, robust transaction ledger1321396>Strategyproof Allocation of Multidimensional Tasks on Clustersd , Library of the School of Science
201409122014 p< . (), , . vThe present thesis focuses on the problem of fair resource allocation in a
system containing multiple machines with multiple resources each. The users
have heterogeneous demands and Leontief preferences, i.e. demand resources in
fixed proportions. Resource allocation is a key issue in the design of cloud
computing systems. Traditional solutions, like maxmin fairness per resource
don t work well in this multi resource setting. Furthermore, efficiency and
fairness are not the only issues here; the designer must take into account the
users incentives.
In the past couple of years this problem has received a lot of attention from
the algorithmic game theory community. We review some the most important
results related to multiresource allocation, starting from the work of Ghodsi
et al ([7]) that studied the problem on a single machine setting with
fractional tasks. We then move on to the indivisible tasks on a single machine
case, studied by Parkes et al ([13]). Finally we discuss the work of Friedman
et al ([4]) that studies the problem of executing indivisible, containerized
tasks on a multiple machine setting.8DRF, Fairness, Resource allocation, Strategyproofness161321290Normalisation in Deep Inference
201112082011 O , AIn this thesis we present the calculus of structures, a prooftheoretic
formalism
using deep inference. This means that inference rules apply arbitrarily
deep inside formulas. It follows that derivations are now symmetric instead
of treeshape objects. A system for classical predicate logic is introduced
and compared with the corresponding sequent calculus system. They both
have an admissible Cut rule. However, locality can be obtained with deep
inference, meaning that the effort of applying a rule is always bounded. Then
we investigate what normal forms of deductions have been defined. Besides
cut elimination, we can adopt two other notions of normalisation that allow
cuts inside a derivation, under some constraints. We will try to remark
common things and differences between normalisation in deep and shallow
inference.Kathematical logic, Proof theory, Deep inference, Calculus of structures71051321056AExpander graphs, randomness extractors and error correcting codes
201409252009 [ (), . . , . The purpose of this thesis is to introduce three important notions of
Complexity, Cryptography and generally Pseudorandomness. We survey the notions
of Expander Graphs, Randomness Extractors and List Decodable Error Correcting
Codes. The former are graphs that on the one hand are very sparse, namely they
do not have many edges, yet on the other hand are very well connected.
Randomness Extractors are function that take as input a string of imperfect
randomness and output a (close to) uniformly random string. List Decodable
Error Correcting Codes have seemingly little relevance with Pseudorandomness.
They try to solve the problem of communication over a network that introduces
higher noise than can be tolerated by simple Error Correcting Codes. The
decoding procedure does not uniquely decode a codeword, but rather gives a list
that includes the original message.
All three objects have their own body of research, each one with seemingly
irrelevant techniques. However, it can be shown that they can be expressed in
terms of the other. That is, Expander Graphs and Randomness Extractors can be
expressed in the language of List Decodable Error Correcting Codes and vice
versa.vPseudorandomness, Complexity Theory, Expander Graphs, Randomness Extractors, List Decodable Error Correcting Codes561321064KExploiting the structure of the data in approximate nearest neighbor search
201208032012! Nearest neighbor searching (NNS) is a fundamental problem with several
important applications.
To accelerate the queries, we exploit the fact that
data often exhibits highly nonrandom spatial patterns.
We consider input points almost lying on about $\log^t n$ unknown lines
in a space of constant dimension $d$,
where $n$ is the number of points and $t$ constant.
The lines are distributed uniformly in a bounding sphere,
the points are distributed uniformly on each line, and their number
per line varies from $\Omega (\log^t n)$ to $O(n)$.
Queries take $O( \log \log n / \epsilon^{O(d^2)})$ expected time, which is
exponentially faster than without structure,
using optimal space $O(n)$, and return a
$(1+\epsilon)$approximate nearest neighbor, for any given $\epsilon>0$.
Ignoring the step of NNS on a line, queries take
$O( \log^2 \log n / \epsilon^{O(d^2)})$ with high probability.
Our key step is to employ a reduction of determining the nearest line
to NNS among points.UNearest line, Aligned points, Structured data, Exponential speedup, Optimal space261318997NonCommutative Cryptography
20160831  5This thesis gives us the opportunity to take a journey to the wonderful world
of Algebra and Group Theory, experiencing a pleasant introduction to the
attracting mysteries hidden behind Cryptography, to its whole extent, from the
Ancient Times until today.We will further investigate specific problems of
Group Theory, with those of conjugation, word and isomorphism being the
cornerstone. We will recall wellestablished cryptography and digital signature
protocols and come across with some of their various weak aspects.This will
inspire us in identifying and studying alternative ways to ensure the security
against malicious attempts, through various tools borrowed from the world of
Groups, like the special case of Braids Group. In this way, we will become more
familiar to forms like Dehornoy and Garside ones, without leaving apart cases
like Matrix Groups, Thompson Groups, Artin Groups and Dehn
Algorithm.NonCommutative Cryptography follows with analysis of various
protocols, with the AnshelAnshelGoldfeld one playing the major role.
Additionally, we will study similar problems and a respectful range of
relations developed among them.Concluding, we will accomplish our journey with
various Decision P< roblems and the Public Key Cryptography, having as leading
characters Shpilrain, Zapata and Tietze.JNonCommutative, Cryptography, NonAbelian, Braid Groups, Group Theory471841309630Doctoral DissertationhFormalizing Constructive Analysis: A comparison of minimal systems and a study of uniqueness principles.Dissertation committee
20121227 PProfessor Joan Rand Moschovakis UCLA, : . ^This dissertation investigates certain aspects of the formalization and
axiomatization of constructive analysis.
The research in the branches of constructive analysis corresponding to the
various forms of constructivism is carried out in a multitude of formal or
informal systems, whose relations are unclear. This problem becomes quite
crucial for the development of the relatively new field of constructive reverse
mathematics. This work contributes to a clearer picture.
Part 1 contains a precise comparison of the two most widely used systems which
formalize the common core of constructive, intuitionistic, recursive and
classical analysis, namely
Kleene's M and Troelstra's EL. It is shown that EL is weaker than M and that
their difference is captured by a function existence principle asserting that
every decidable predicate of natural numbers has a characteristic function.
Applying similar arguments, comparisons of most of the used minimal systems are
obtained.
In constructive analysis, various forms of choice principles, continuity
principles and many others are used. Part 2 studies relations between many of
them, in their versions having a
uniqueness condition, a feature from which interesting properties follow, as
well as relations between these principles and nonconstructive logical
principles, in the spirit of reverse
mathematics.?Analysis, Constructive, Formalization, Axioms, Secondorderviii, 9013213187Opinion dynamics in the presence of social choice rules
20141118  f . (), , . xNetworks rise in several aspects of modern life, motivating us to model and
understand them. Several types of mathematical and algorithmic problems arise
in networks. Opinion dynamics is a process in networks modelling the effect of
local interactions on agents' beliefs. The beliefs can be thought as a belief
for some common question of interest, for instance the probability of some
event. In this thesis, I will present mathematical models which capture such
processes in networks and state mathematical problems on them. I try to
evaluate these processes in terms of economic behavior and convergence time of
dynamic processes.
We would ideally like to connect these quantities with parameters of the
network structure. Finally, motivated by polls present
on political elections, we study the effect of partial global information on
agents' local interactions and behavior.RNetworks, Social Networks, Game Theory, Social Choice Theory, Opinion Dynamics231321343Randomlyoriented RKDtrees
20141204 . 9Consider a set S of points in a real Ddimensional space R^D, where distances
are defined using function : R^D R^D > R (the Euclidean metric). Nearest
neighbor search is an optimization problem for finding the closest points in S
to a given query point q R^D . Given a positive real >0, then a point p S
is a (1 + )approximate nearest neighbor of the query point q R^D if dist(q,
p) (1 + )dist(q, p_nn) where p_nnS is the true nearest neighbor to q. If
the data that is expressed in highdimensional space R^D lies closer to an
embedded manifold M of dimension d, where d<<D, then, we show the data may be
preprocessed into the Randomlyoriented RKDtrees structure and we provide a
near optimal bound on the number of levels required to reduce the size of its
cells by a factor s2. We show the data may be preprocessed into the structure
in O(D N log N) time and O(D N) space, so that given a query point qR^D
and >0, a (1+ )approximate nearest neighbor of q may be reported in O((D/)
^O(d log (d) log (d D/)) log N) time. Following the theoretical results, we
show that the methods presented offer a highly efficient implementation in
highdimensional ANN search. Our implementation extends the Computational
Geometry Algorithms Library (CGAL) and more specifically the spatial searching
package of the library. The experimental results show that the proposed
algorithm offers a state of the art ANN search algorithm when searching among
highdimensional data and highdimensional data with an underlying
lowintrinsic dimensional subspace.Nearest neighbor searching, Approximate nearest neighbor searching, Approximation algorimths, Postoffice problem, Priority search71133831321464$Visual Cryptography and Applications
201509292015 . Visual Cryptography is an encryption technique for visual information such
as images or text, based on the secret sharing problem. The secret is
encrypted in such a way that its decryption is very simple since there is
no need for any mathematical calculations: it is done automatically by the
human eye. Furthermore, the secret is completely safe since it cannot be
revealed by any unauthorized opponent, even one with infinite
computational power. The first concrete definition of k out of n visual
secret sharing schemes was stated in Visual Cryptography by Moni Naor
and Adi Shamir alo< ng with specific applications and extensions of the
initial model. Two more constructions and properties of k out of n visual
secret sharing schemes are presented in Constructions and Properties of k
out of n Visual Secret Sharing Schemes by Eric R. Verheul and Henk C. A.
Van Tilborg. Additionally, an introduction to the notion of coloured
visual secret sharing schemes is introduced. This thesis studies the above
mentioned papers, makes an introduction to Visual Cryptography and
Coloured Visual Cryptography. furthermore, it describes some
constructions, and some of the basic applications of Visual Cryptography.dVisual Cryptography, Coloured Visual Cryptography, Applications, Visual secret , Sharing schemes1251321458MVariants of stable marriage, algorithms, complexity and structural properties
20111220 C . . , Since 1962, when the Stable Marriage Problem was first proposed by David Gale
and Lloyd Sharpley, there have been many theoretical results as
well as numerous applications. Also, numerous variants of the problem have been
proposed, thus establishing a very interesting class of problems. This thesis
is a thorough review of the literature, concerning Stable Marriage and its
variants, concentrating on the algorithmic, complexity and structural results
that have been published so far. Also, a new result is presented, namely, an
upper bound on the maximum number of stable matchings for the Stable Marriage
problem and,
via reductions this bound is extended to the HospitalResidents and Stable
Roommates problems.kStable Marriage, Variants of Stable Marriage, Maximum number of stable matchings, Complexity, Structure66X, 531321460(Variants of Stalnaker Stable Belief Sets
20141202 hK/ ... / , / . / We vary the context rules underlying the positive and/or negative introspection
conditions in the original definition of R. Stalnaker, to obtain variant
notions of a stable epistemic state, which appear to be more plausible under
the epistemic viewpoint.
For these alternative notions of stable belief set, we obtain representation
theorems using ossible worlds models with nonnormal (impossible) worlds and
neighborhood modal models.
En route, we identify some modal axioms which appear to be of some interest in
KR and develop the proof theory of some regular and classical modal logics with
a notion of strong provability. This stream of research resembles the questions
posed and (partly) settled in classical (monotonic) epistemic reasoning about
logical omniscience, now examined under the perspective of
Knowledge Representation. Additionally we investigate the minimal knowledge
approach of HalpernMoses only knowing in the context of the aforementioned
syntactic variants.iNonmonotonic logic, Epistemic logics, Modal logic, Knowledge representation, Artificial Intelligence1321308MOn the computability of obstruction sets for wellquasiordered graph classes
20120918 ( , In this MSc thesis we are going to present algorithms for computing obstruction
sets of wellquasiordered graph classes. Neil Robertson and Paul Seymour's
Graph Minor Theorem (GMT) guarantees that any minorclosed graph class has a
finite obstruction set. If C is such a class, the obstruction set of C is the
minimal set of graphs H such that G belongs to C if and only if none of the
graphs in H is contained as a minor in G. The analogous result for another
wellquasiordering, the immersion ordering, was shown in the same series of
papers (Graph Minors). But these results are nonconstructive; we know that a
minor or immersionclosed graph class has a finite obstruction set but the GMT
does not imply any algorithm for computing it. K. Cattell, M. J. Dinneen, R.
Downey, M. R. Fellows and M. Langston in "On computing graph minor obstruction
sets" and I. Adler, M. Grohe and S. Kreutzer in "Computing Excluded Minors"
present algorithms to overcome this problem for minorclosed graph classes, as
well as, applications of their methods proving that the obstruction sets of
various graph classes are computable, such as the union problem. By adapting
some of the methods of Adler, Grohe and Kreutzer to immersions, the analogue
result for immersion obstruction sets and an algorithm for the union problem on
immersionclosed graph classes are proven by A. Giannopoulou, D. Zoros and the
author, under the supervision of D. M. Thilikos.[Graph Minor Theorem, Obstruction set, Monadic SecondOrder Logic, Immersions, Treewidth31481321310)On the meaningful instances of clustering
20150212
g (), , . Clustering is a problem with many different definitions, approaches and
applications, but not well
defined mathematically. Especially it is not clear how to define
meaningfulness, and how to determine
if a solution is meaningful, in the sense that it reveals some existing
inherent in the data
structure.
When we refer to clustering via optimization of some objective functions, it is
usually a task
performed efficiently, despite that most existing objective functions are
NPhard.
We will present some existing results showing that meaningful instances can
be solved efficiently.
In these papers is made app< arent (implicitly or explicitly) a connection
between structure in
the data, and the behavior of the objective function over the space of
solutions.
We will propose a method exploiting this connection, that could decide for each
pair fobjective
function, datasetg, if it is meaningful the particular dataset to be
clustered by optimizing (or approximating)
this particular objective function.Clustering, Clusterability361321312/On the relation between treewidth and toughness
20120905 JThe problems of computing the treewidth and the toughness of a graph are
wellknown NPhard problems.
Treewidth is a measure of connectivity in graphs as well as a measure of
efficient computing
for wellknown NPhard problems defined in graphs. Tougness on the other hand
is a measure of acyclicity of a graph
as well as an indicator parameter for the existence of cyclic structures in
graphs. In this Master's thesis, we
relate these two graph paramers, giving some upper bounds on toughness as a
function of treewidth and justify
that there does not exist a similar lower bound.Treewidth, Toughness, Graph138781321337Proofs of Secure Erasure
201301082013 ! . We investigate the problem of verifying the internal state of a remote embedded
device (remote attestation), using what was by Tsudik and Perito introduced as
Proofs of Secure Erasure. This is a procedure that has to take place in many
cases, ranging from wireless sensor networks to any device running a software
update: One has to make sure that even a compromised device will erase all of
its memory contents when asked to, leaving no part of it left unaltered,
possibly running malicious software. The protocols proposed thus far demand
either very high communication complexity or very high time complexity that
renders them ineffective for most practical applications.bSecure erasure, Space complexity, Time space tradeoffs, Superconcentrators, Function inversion6113213635Secure multi party computations for electronic voting
20140508 z . (), , . In this thesis, we study the problem of electronic voting as a general decision
making process that can be implemented using multi party computations,
fulfilling strict and often conflicting security requirements. To this end, we
review relevant cryptographic techniques and their combinations to form voting
protocols. More specifically, we analyze schemes based on homomorphic
cryptosystems, mixnets with proofs of shuffles and blind signatures. We analyze
how they achieve integrity and privacy in the voting process, while keeping
efficiency. We examine the types of social choice functions that can be
supported by each protocol. We provide two proof of concept implementations.
Moreover, we review ways to thwart stronger adversaries by adding receipt
freeness and coercion resistance to voting systems. We build on the latter
concept to propose a modification to a well known protocol. Finally, we study
two actual eVoting implementations namely Helios and Pret a Voter .`Electronic Voting, Homomorphic Cryptosystems, Proofs Of Knowledge, Mixnets, Blind Signaturesvii141vii, 1341321083F
20150327 v . (), . , .. <Game Theoretic Models for Power Control in Wireless NetworksIn recent years, the technology of mobile communications has evolved rapidly
due to increasing requirements, such as access to Internet services via mobile
phones and requirements better quality services. Nowadays, the devices use the
Long Term Evolution (LTE), which called also as 4G networks. The fourth
generation (4G) networks replace the third networks generation (3G) and offer
to users improved services at higher speeds. Mobile devices to access the
Internet, such as smartphones, tablet PCs and netbooks are in high demand in
the market for it is an effort to develop in energy consumption level, that the
user does not need recharge the device at regular time intervals. Game theory
provides valuable mathematical tools that can be used to solve problems of
wireless communication networks and can be applied to multiple layers of
wireless networks.
In this thesis, we study power control issue and consider it at the physical
layer of wireless networks. Specifically, we study game theoretic models for
power control in wireless communication networks (CDMA & LTE). In the game
theory, we have focused in the noncooperative power control games and assumed
that both transmitters and receivers are selfish and rational. In addition, we
insert regret learning techniques and their connection with the game theory.
Finally, we investigate the regret learning techniques applied to the problem
of power control in the next generation networks._Game Theory, Power Control, Regret Learning Algorithms, Wireless Networks, LTE/LTEAdvanced91081321089>Generalized SecondPrice Auctions under Advertisement Settings
20130307 At the current M.Sc thesis we study Generalized SecondPrice Auctions under
advertisement settings. In chapter 1 we make an introduction to the basic
concepts of the auctions, presenting several auction models and analyzing their
properties. We proceed in chapter 2 studying the equilibria properties of the
GSP auction under the advertisement position setting. We provide several
notices and additional proofs regarding the comparison between the pure Nash
equilibria and EnvyFree equilibria. In chapter 3 we study the notion of budget
and observe the Budgeted SecondPrice advertisement auction.
In section 3.6 we display notices and some results from our side. Additionally
we examine
the critical bid notion under the same setting when the items are not
divisible. Finally we conclude with chapter 4, introducing two GSP auction
models customized under budget constraints. We analyze the structure of the two
models and provide proofs regarding their
equilibria properties.@SecondPrice Auctions, Equilibrium, Budget, Ad Setting, Slot941319006b
20120730 /. ()ZIn this thesis, we initially provide a general introduction to pairingbased
cryptography, consisting of the presentation of the established methods for
constructing and computing a pairing and some of the most fundamental
pairingbased schemes and protocols. We then focus on the analysis of the
seminal GrothSahai system for the construction of efficient noninteractive
NIWI and NIZK proofs. Finally, we examine
the applications of the < GrothSahai proof system to group signature schemes and
especially their contribution to achieving the required security properties
without random oracles.9Pairing, Cryptography, GrothSahai, Group, Signatures18217713193528Obstructions and Algorithms for Graph Searching Problems
20140204 w. . (), , . F? ? ? ? ?Graph Searching is a field of Discrete mathematics with numerous applications
in many areas of Theoretical Computer Science. It Is also of great theoretical
interest as it formalizes many important combinatorial problems. We present the
motivations which led researchers to graph searching, we typically define the
three basic types of searching, and we introduce some of the major variants.
Then we analyze the concepts of monotonicity and connectivity and record some
results from the literature. Next we study the Theory of Partial Orders on
graph classes and how this is associated with the characterization of some
classes through a set of forbidden graphs, called obstruction Set of the class.
After briefly mentioning the necessary concepts, we present all so far known
obstruction sets for classes of graphs with bounded search number. The larger
set to be mentioned is included in the results of our work, which is still
under preparation. Graph searching is closely related to the Width Parameters
of a graph. Most of the results in the literature concern these parameters, as
their terminology eases the proofs of the theorems. In Chapter 6 we define some
important width parameters and we illustrate how they relate to the search
number of the graph. The third part of this work consists of the study of the
Computational Complexity of some graph searching problems. Finally we make a
brief presentation of our results and the core ideas underlying their proofs.UObstruction sets, Graph Searching, Algorithms, Discrete Mathematics, Graph Theoryiiiiv49iv, 681308878u . , .
20121002 ,() , , The first chapter begins with a survey on the epistemic modal logics (EML) of
Lenzen and Stalnaker, continues with a presentation of the equivalent EML S4.2
and of the dominant definition of belief based on knowledge, and describes,
finally, the Kripke models of S4.2. In the second chapter, the KBpstructures
are being introduced in contrast to Stalnaker s stable theories, it is proved
that negative introspection does not hold for them and that they are consistent
with S4.2. Next, characterization theorems of KBpstructures by S4.2 are
proved. In the third chapter, the bimodal logic KBE is defined, using a modal
language, which in addition to the operators K and B (representing knowledge
and belief, respectively) is endowed with an operator E, describing estimation.
Furthermore, weak ultrafilters are introduced, which are used for defining the
kbeframes and models, which are Kripkestructures w.r.t. K, and modified
general ScottMontaguestructures w.r.t. E. Finally, there are proved some
characteristic properties of KBE and soundness / completeness of KBE w.r.t. the
kbeframes. In the last chapter, it is attempted, using an EML, to capture the
epistemic change of an agent (i.e. what she knows / believes / estimates)
caused by new information received from different sources. So, the modal
language of KBE is expanded in order to contain two copies of its operators
(describing the situation before and after the information reception), and new
operators I, one for each information source. Then, the logic KBEI is defined
with the intention to describe this dynamic situation, and there are proved
some expected properties of it. Finally, the kbeiframes and models are
introduced, and soundness / completeness of KBEI w.r.t kbeiframes is proved.]Epistemic Modal Logic, Kripke Models, Negative Introspection, Stable Theories, Estimation8586VIII, 861319511*When is it possible to aggregate opinions?
20160624 Q (), , ) ;We consider a population that wants to decide what to do over some issues. We
explore the connection between aggregating their votes in a nondictatorial
manner with the complexity of the satisfiability problem defined over the set
of feasible voting combinations.VAggregation, Possibility domain, SAT, Multisorted relation, Conservative function1320940>Complexity dichotomies for approximations of counting problems
20120727! g (), . , xThis thesis is a survey of dichotomy theorems for computational problems,
focusing in counting problems. A dichotomy theorem in computational
complexity, is a complete classification of the members of a class of problems,
in computationally easy and computationally hard, with the set of problems of
intermediate
complexity being empty. Due to Ladner's theorem we cannot find a dichotomy
theorem for the whole classes NP and #P, however there are large subclasses of
NP (#P),
that model many "natural" p< roblems, for which dichotomy theorems exist.
We continue with the decision version of constraint satisfaction problems
(CSP), a class of problems in NP, for which Ladner's theorem doesn't apply. We
obtain a
dichotomy theorem for some special cases of CSP. We then focus on counting
problems presenting the following frameworks: graph homomorphisms, counting
constraint
satisfaction (#CSP) and Holant problems; we provide the known dichotomies for
these frameworks.
In the last and main chapter of this thesis we relax the requirement of exact
computation, and settle in approximating the problems. We present the known
cassification theorems
for cases of #CSP. Many questions in terms of approximate counting problems
remain open.
The appendix introduces a recent technique for obtaining exact polynomialtime
algorithms for counting problems, namely the holographic algorithms.Computational Complexity, Counting Complexity, Dichotomy Theorems, Approximation Algorithms, Constraint Satisfaction Problem63iv, 511320942+Complexity dichotomies of counting problems
20120724 G. . , . , . nIn this thesis we study dichotomy theorems mainly of counting problems. A
dichotomy theorem for a class of problems, in computational complexity, is a
complete classification of the problems of this class in computationally easy
and computationally hard problems, without intermediate problems. Due to
Ladner's theorem we cannot find a dichotomy for the whole classes NP and #P,
however there are large subclasses of NP (#P), that model many "natural"
problems, for which dichotomy theorems exist. We begin with the framework of
the decision version of constraint satifaction problems (CSP) and then we study
the classes of graph homomorphisms problems, of counting constraint
satisfaction problems (#CSP) and of Holant problems. Finally, we will make a
brief introduction to holographic algorithms, a special type of polynomialtime
algorithms for counting problems.lDichotomy, Constraint Satisfaction Problem, Graph Homomorphisms, Holant Problems, Holographic Algorithms40viii, 541320946Computational Aspects of the Braess's Paradox
20150330 p . () , , . SIn this thesis, we investigate the Braess's Paradox from a computational
viewpoint. The motivation is to provide simple ways of improving network
performance by exploiting the essence of the Braess's Paradox, namely the fact
the network performance at equilibrium can be improved by edge removal. We
first present approximation algorithms for the best subnetwork problem in
random networks with linear latencies and polynomially many paths, each of
polylogarithmic length. Moreover, we improve on the best known running time for
the best subnetwork problem in certain classes of networks.[Braess's Paradox, Best Subnetwork, Random Networks, "Good" Networks, Computational Time13913209447Computability and complexity of twoway finite automata
20130531 8. . ., . . .:Computability of finite automata with one head, and computational equivalence.
Complexity classes of those finite automata, complete problems, open problems,
reductions, relations with turing machine complexity. Search for a reduction,
to find a complete problem in classes with constant input. Counterexamples.CComputability, Complexity, Automata, Nondeterministic automaton17621320955?Counting below #P: Classes, problems and Descriptive Complexity
20160923 f , . (), . In this thesis, we study counting classes that lie below #P.
One approach, the most regular in Computational Complexity Theory, is the
machinebased approach. Classes like #L,
spanL and TotP, #PE are defined establishing space and time restrictions on
Turing machine's computational resources.
A second approach is Descriptive Complexity's approach. It characterizes
complexity classes by the type of logic needed to express
the languages in them. Classes deriving from this viewpoint, like #FO,
#RH_1, #R_2, are equivalent to #P, the class of APinterriducible
problems to #BIS, and some subclass of the problems owning an FPRAS.
A great objective of such an investigation is to gain an understanding of how
efficient counting relates to these already defined classes.
By efficient counting we mean counting solutions of a problem using a
polynomial time algorithm or an FPRAS.
Many other interesting properties of the classes considered and their problems
have been examined. For example alternative definitions
of counting classes using relationbased operators, and the computational
difficulty of complete problems, since complete problems capture
the difficulty of the corresponding class. Moreover, in Section 3.5 we define
the logspace analog of the class TotP and explore how and to
what extent results can be transferred from polynomial time to logarithmic
space computation.QComputational complexity, Counting, Logspace, Descriptive complexity, spanL58801320957UCounting complexity: compressed amming distance, vertex covers and recent highlights
20150506 f . (), , . XIn this article, we tackle the compressed Hamming distance problem. The Hamming
distance is an easy problem, but when we move to a compressed input (via the
SLP compression method) the problem becomes #Pcomplete. We propose a range of
algorithms for specific cases of the problem. Secondly, we deal with the
counting vertex covers problems in paths,cycles and trees, and answer more
specific questions like the probability of a vertex being part of a cover, and
the number of covers for any specific size Cryptography, Elliptic, Curve, Digital signatures, Bitcoin9113174598Heuristic Algorithms for the Tourist Trip Design Problem
20140328 f (), , . I A tourist does not have enough time to visit all attractions of the
destination. Hence, she has to decide which to visit and plan the daily routes
of the trip. Tourist Trip Design Problem (TTDP) asks for the most pleasant
routes for the tourist. TTDP is modelled as the Orienteering Problem (OP),
which is NPhard, or extensions of OP. In OP a set of nodes is given, each
associated with profit, and asks for the route with the maximum collected
profit and length bounded by a given time budget. TOPTW extends OP asking for
multiple routes, allowing the visit at nodes to take place within specified
time intervals. TDTOPTW extends TOPTW considering time dependent travel costs.
In this thesis novel heuristic algorithms are presented for TOPTW and TDTOPTW.
The algorithms aim at producing near optimal solutions within fast execution
time. Two new heuristic algorithms CSCRatio and CSCRoutes are presented for
TOPTW, while new heuristic algorithms, that extend CSCRoutes to incorporate
time dependent travel costs, are proposed for the TDTOPTW. The proposed
algorithms are compared with the most efficient until now algorithms in
existing instances and in new, created to simulate realistic tourist
topologies.]Heuristic Algorithms, Tourist Trip Design, Time Budget, Time Windows, Profit Maximization877113175647Smart contracts and Payments using Bitcoin and Ethereum
20150612 0 , B Bitcoin EthereumThis Thesis focuses on Bitcoin ,a digital currency, which was proposed by
Satoshi
Nakamoto [3] in 2008 . We describe both its function and its security [1],[2].
Bitcoin
is a cryptocurrency, which is decentralized, as there is not any trusted
authority that
mints coins or controls transactions. Consequently, we describe some smart
contracts
[12], which use Bitcoin to solve problems of trust. In addition, we study a
construction (and its security) , Zerocoin [22], which can be implemented in
Bitcoin
in order to achieve anonymity (it was proposed by Ian Miers, Christina Garman,
Matthew Green, Aviel D. Rubin in 2013) ,as well as a dynamic accumulator
published by J. Camenisch and A. Lysyanskaya [23] that is used in the above
construction . Finally, we analyze Ethereum s function .Ethereum is a
decentralized
system that uses a Turing complete language in order to make the contract
creation
easier and was proposed by Vitalik Buterin and Gavin Wood [20],[21] in 2013
2014.8Cryptography, Contracts, Bitcoin, Ethereum, Zerocoin931317363Scientific realism and modality in abduction.
20160122 & 8 In this thesis we study the formalization of abduction in modal frames. Over
the last decade researchers focus on modal frames. The typical modal operators
can formalize the diversity between knowledge and beliefs. Also, we can
construct some manyworld models of ascending cardinality. Our main issues are
the criteria of selecting the best explanation and their possible correlation.
In introduction we sketch some abductive inferences and show some applications
in science and philosophy. The second chapter contains a vast presentation of
selective abductions due to Schurz and a brief presentation of some explanatory
virtues. The third chapter contains the manyworld approach of SolerToscano,
FernandezDuqueand NepomucenoFernandez. In the fourth chapter we present the
dynamic proofs approach, as defined by Gauderis. Chapter 5 and 6 consist in a
brief discussion of these models. We examine if they formalize every possible
selective abduction and if they satisfy any of the explanatory virtues. Chapter
7 contains an alternative approach for formalizing consilience. The final
chapter contains the conclusion and some open problems.XAbductive Inference, Scientific Realism, Modal Logic, Explanatory Virtues, Parsimony251321133TImplementing approximate voronoi diagrams for approximate nearest neighbor searching
20120822  Nearest neighbor searching
is a fundamental problem in computer science. One of the main theoretical
issues is to balance
query time and space complexity: the recent Approximate Voronoi Diag< ram (AVD)
leads to
optimal query time while making the tradeoff with space usage explicit.
The key idea is to cluster the space around the input points and use
boxes of varying size to cover it. Each cluster is assigned a subset of
the points, which are candidate approximate nearest neighbors
to every point in that cluster.
However, the implementation of AVD has been a daunting task and was never
completed.
We offer the first, efficient, parallel implementation of the AVD which accepts
dimension as input and introduce certain ideas and
modifications that make the construction feasible. In our experimental results,
we show that our data structure is much faster and more accurate than
a standard KDtree in low dimensions.gApproximate Nearest Neighor, Approximate Voronoi Diagram, Optimal Query Time, KD/BBD Tree, Quadtree461321199Linkages in primaldual graphs
20160615 .
One of the most influential bodies of work in Graph Theory has, undoubtedly,
been the Graph
Minor
series of Neil Robertson and Paul D. Seymour, where,
after 23 papers during the years 19832011, they managed to prove Wagner's
conjecture. This conjecture states that undirected graphs, partially ordered by
the graph minor relationship, form a wellquasiordering, or, equivalently,
every
family of graphs that is closed under minors can be defined by a finite set of
forbidden minors. One can argue that it is not just the final result itself, but
whole theory built during the procedure which had, and continues to have, a
huge impact in both combinatorial and algorithmic Graph Theory. One of their
main contributions, which also has a central role in their work, is constructing
an algorithm that solves the Disjoint Paths problem in f(k)n^3 steps, where
k is the number of disjoint paths that we are asked to find. The key ingredient
of their proof is the so called irrelevantvertex
technique (for which full proofs
only appeared in latter parts of the series), which has been used extensively
thereafter.
As great as this result was proved to be, the function f of k that appears in
the running time is immense even for very small values of k. Therefore, many
researchers tried to improve this parametric dependance on k, either by trying
to simplify the complicated proofs of the structural theorems for the general
case, or by restricting their attention to specific graph classes whose
structural
characteristics would hopefully lead to simpler proofs and better parametric
dependance. A big step towards the first direction (although the bound of f(k)
is 2^(2^(2^(2^(k))))
which is of course still huge) was made by Kenichi Kawarabayashi
and Paul Wollan in [20]. A decisive step to the second direction, for the class
of planar
graphs, was made by Isolde Adler, Stavros G. Kolliopoulos, Philipp
Klaus Krause, Daniel Lokshtanov, Saket Saurabh, Dimitrios M. Thilikos in [2],
where their bound for f(k) is just single exponential on k.
Based on this latter work, we study an extension of the Disjoint Paths problem
for the class of pdgraphs and, using on the idea of the irrelevantvertex
technique, we prove a structural theorem which states that if the treewidth of
our pdgraph is sufficiently large, then there exists (and can be found
algorithmically)
a part of it which is irrelevant and whose removal leads to a simpler
and equivalent instance. We also illustrate how an algorithm for the Disjoint
Paths problem for the class of pdgraphs can be used to construct algorithms
for problems on plane graphs, where the it is essential to respect the topology
of the plane embedding given as an input.ELinkage, Primaldual, Irrelevant vertex, Disjoint paths, Pdgraph5721321201" "
20150713
( . (LiquidHaskell : Liquid Types for HaskellEven welltyped programs can go wrong, by returning a wrong answer or throwing
a runtime error. A
popular response is to allow programmers use refinement type systems to express
semantic specifications
about programs. We study verification in such systems. On the one hand,
expressive refinement
type systems require runtime checks or explicit proofs to verify
specifications. On the other, less expressive
type systems allow static and automatic proofs of the specifications. Next, we
present abstract
refinement types, a means to enhance the expressiveness of a refinement type
system without increasing
its complexity. Then, we present LiquidHaskell that combines liquidTypes with
abstraction over
refinements to enhance exp< ressiveness of LiquidTypes. LiquidHaskell is a quite
expressive verification
tool for Haskell programs that can be used to check termination, totality and
general functional
correctness. Finally, we evaluate LiquidHaskell in real world Haskell
libraries.]Programming languages, Refinement Types, Abstract Interpretation, Algorithmic Verification521321099*Graph partitioning under the spectral lens
20150123 v (), . , . Finding underlying structure in data has been a fundamental task for
mathematicians, computer and now datascientists and the importance of
clustering and partitioning data has increased dramatically in the past decade.
We present the journey of one of the most essential problems in the area: Graph
Partitioning. We begin with the importance and the wide range of applications
it finds, the computational difficulties involved in solving it efficiently and
the inapproximability results tied to it. We demonstrate the first average case
analysis approaches using random models, the most prominent of which is the
planted partition model or stochastic block model where the graph has k equally
sized blocks and vertices connect independently with probability p within
blocks and q across blocks. Recently, a large amount of research in computer
science and statistics has been invested in providing lowerbounds on the
scaling of p q to ensure recovery of the planted blocks (partitions). We
focus on the seminal results using spectral techniques and provide a high level
overview of this rapidly evolving area, including the recent
informationtheoretic perspective threshold on the p q range for recovery.
Finally, give our own spectral approach for solving Graph Partitioning for
arbi trary k in the planted partition model and albeit not improving the
stateoftheart we believe our approach constitutes a new, easier proof for a
very recent result.DAlgorithms, Complexity, Spectral Graph Theory, Graph PartitioningVII,461321210QLowquality dimension reduction and highdimensional Approximate Nearest Neighbor The approximate nearest neighbor problem (ANN) in Euclidean settings is a
fundamental
question, which has been addressed by two main approaches: Datadependent space
partitioning
techniques perform well when the dimension is relatively low, but are affected
by
the curse of dimensionality. On the other hand, locality sensitive hashing has
polynomial
dependence in the dimension and sublinear query time.
We generalize the JohnsonLindenstrauss lemma to define lowquality mappings
to a
Euclidean space of significantly lower dimension, such that they satisfy a
requirement weaker
than approximately preserving all distances or even preserving the nearest
neighbor. This
mapping guarantees, with constant probability, that an approximate nearest
neighbor
lies among the k approximate nearest neighbors in the projected space. This
leads to an efficient
randomized tree based data structure that avoids the curse of dimensionality.fData structures, Curse of dimensionality, Nearest Neighbor, Dimension reduction, Random projection911411316314*Decidability and complexity of modal logic
20140501 . . (), . , . , . . 5 In the present dissertation we study modal logic, with an emphasis on its
applications in computer science. One of the most important reasons for the
wide use of modal logic in many areas of computer science (and other
disciplines) is its behaviour with regard to decidability: modal logic is
decidable and remains decidable after many powerful extensions while, at the
same time, it is expressive enough to be useful in practice. One could
juxtapose this behaviour with the behaviour of firstorder logic, which is even
in the simplest case undecidable. Moreover, even though the computational
complexity of modal logic is in theory very high, in practice the problems that
force such complexity are very rare. Initially we present relevant results, and
we then try to interpret this behaviour by considering relevant fragments of
firstorder logic, which effectively express the "spirit" of modal logic.vModal logic, Computability theory, Computational complexity, Fragments of firstorder logic, Twovariable fragmentiv, 531316443"Perpetual reductions in calculus
20140124 o () , ! Perpetual reductions are a tool which has contributed to the comprehension of
some properties of reduction. An important application of this tool concerns
the proof of theorem by Sorensen, whereas another one is about the
characterisation of the perpetual redexes of a term. An alternative way of
proving these is the method of assigning types to terms, which we study in the
last chapter of this theses.HReductions, Strategies, Perpetual, Type assignment, Sorensen theorem4[14], 8113181279Centralized protocols and anonymous decentralized systems 1 , B In the present thesis, firstly we study the centralized protocol of the blank
signature
[23], a new type of signature that was published by Christian Hanser and Daniel
Slamanig , in 2013,as well as the security of this scheme. The existence of
centralization in the above protocol, as we will see, is a crucial part because
if we
ignore it, one of the participants can find a trapdoor to the protocol.
Consequently we
refer to the decentralized protocol of Bitcoin [3] that was published by Satoshi
Nakamoto ,in 2008 ,as well as the< security with which it provide us [1],[2] ,
and
we also refer to some smart contracts [12] that has been built on top of this
,which use its decentralized character. Lastly, we refer to the new
decentralized
system, the Ethereum[21],[22], that was introduced by Vitalik Buterin, Gavin
Wood ,in 20132014 (during this thesis ,its development has been growing),which
advantages it wants to achieve in comparison with the Bitcoin as well as the
formal way of its function .BCryptography, Ethereum, Bitcoin, Digital signatures, Contracts1321263NModeltheoretic investigations on `overwhelming majority' default conditionals
20151120 K (), . Defeasible conditionals of the form `if A then normally B' are usually
interpreted with the
aid of a `normality' ordering between possible states of affairs: A=>B is true
if it happens
that in the most `normal' (least exceptional) Aworlds, B is also true. Another
plausible
interpretation of `normality' introduced in nonmonotonic reasoning dictates
that A=>B is
true iff B is true in `most' Aworlds. A formal account of `most' in this
majoritybased
approach to default reasoning has been given through the usage of weak filters
and weak
ultrafilters, capturing at least, a basic core of a sizeoriented approach to
defeasible reasoning.
In this paper, we investigate defeasible conditionals constructed upon a notion
of `overwhelming majority', defined as `truth in a cofinite subset of ', the
first infinite ordinal. One approach
employs the modal logic of the frame (,<), used in the temporal logic of
discrete linear
time. We introduce and investigate conditionals, defined modally over (,<);
several modal
definitions of the conditional connective are examined, with an emphasis on the
nonmonotonic
ones. An alternative interpretation of `majority' as sets cofinal (in ) rather
than cofinite
(subsets of ) is examined. For all these modal approaches over (,<), a
decision procedure
readily emerges, as the modal logic KD4LZ of this frame is wellknown and a
translation of
the conditional sentences can be mechanically checked for validity. A second
approach employs
the conditional version of ScottMontague semantics, in the form of many
possible worlds,
endowed with neighborhoods populated by its cofinite subsets. Again, different
conditionals
are introduced and examined. Although it is difficult to obtain a completeness
theorem (since
it is not easy to capture `cofinitenessin' syntactically) this research
reveals the possible
structure of `overwhelming majority' condition
!"#$%&'()*+,./0123456789:;<=>?@ABCDEals, whose relative strength is
compared to (the conditional logic `equivalent' of) KLM logics and other
conditional logics in the literature.@Nonmonotonic, Reasoning, Defeasible, Conditionals, Normality7013210380Encryption mechanisms for multiuser environments
20120914 . .As the title indicates, this thesis is related to the role of encryption in
multiuser environments. Specifically, we
concentrate on issues related to a class of encryption schemes called Broadcast
Encryption. Assume that a sender wishes to send messages to a large group of
recipients via a broadcast channel in a way that he
can choose a subset from a set of designated receivers on the fly and enable
them to decrypt a ciphertext while simultaneously preventing any
other party from doing so. The schemes that achieve this goal can be divided
into two categories, combinatorial schemes and schemes based on algebraic
structures, structured schemes. We refer to several examples of each category
with different performance tradeoffs. Furthermore, we provide the necessary
security definitions for these schemes.
The stateoftheart broadcast encryption schemes do not aim to address the
feature of privacy, i.e. in each transmission they do not hide the enabled set
which means that the revoked users can learn the members of the enabled set
even though they cannot decrypt the message. The main part of this thesis
focuses on the feature of privacy in the setting of broadcast encryption. We
present work that has been done related to this property
and then we present
some new results which came up during the preparation of this thesis.
We provide a definitional framework for privacy notions and then we proceed by
giving some lower bounds on the
ciphertext length for private broadcast encryption schemes with respect to the
stated privacy definitions. Our main result is an impossibility result that
highlights the cost of privacy in the ciphertext size for atomic broadcast
encryption schemes (which include the class of combinatorial schemes).Broadcast encryption, Privacy, Lower bounds1321426The discrepancy problem
20111229 a , . , In this thesis, we examine the combinatorial discrepancy problem, we showed
that it is O(\sqrt{n}) and we mentioned randomized algorithm that finds a
coloring of ordering O(\sqrt{n})(Discrepancy, Partial Coloring, Entropy1321415Tamper resilient circuits
20141201 . This dissertation studies the effect of gatetampering attacks against
cryptographic circuits. The proposed adversarial model is motivated by the
plausibility of tampering directly with circuit gates and by the increasing use
of tamper resilient gates among the known constructions that are shown to be
resilient against wiretampering adversaries. We prove that gatetampering is
strictly stronger than wiretampering. On the one hand, we show that there is
a gatetampering strategy that perfectly <simulates any given wiretampering
strategy. On the other, we construct families of circuits over which it is
impossible for any wiretampering attacker to simulate a certain gatetampering
attack (that we explicitly construct). We also provide a tamper resilience
impossibility result that applies to both gate and wire tampering adversaries
and relates the amount of tampering to the depth of the circuit.
Finally, we show that defending against gatetampering attacks is feasible by
appropriately abstracting and analyzing the circuit compiler of Ishai et al. in
a manner which may be of independent interest.
Specifically, we first introduce a class of compilers that, assuming certain
well defined
tamper resilience characteristics against a specific class of attackers, can
be shown to produce tamper resilient circuits against that same class of
attackers. Then, we describe a compiler in this class for which we prove that
it possesses the necessary tamperresilience characteristics against
gatetampering attackers.+Tamper resilient circuits, Attack modelingVI, 501321387>Spherecut decompositions and dominating sets in planar graphs m (), . , An important result in Graph Theory is the proof of Wagner's Conjecture by Neil
Robertson and Paul D. Seymour in Graph Minor Series from 1983 until 2011. This
conjecture state that there is no innite antichain in the class of graphs
under
the minor relation. The theory that was built for the proof of this conjecture
had,
and continues to have, an important impact not only in structural and
algorithmic
Graph Theory, but also in other elds such as Parameterized Complexity.
In the context of this proof, the authors have introduced some new width
parameters. Within these were branchwidth and branch decompositions. This
parameter was used for algorithm design via the \divide and conquer" technique.
Moreover, the authors have introduced, similar to branch decompositions,
concepts
such as spherecut decompositions which are a special type of branch
decompositions
in planar graphs that have some additional properties.
In the course of the research there was a lot of important results about
branchwidth
in the class of planar graphs. Fedor V. Fomin and Dimitrios M. Thilikos
proved that the branchwidth of a nvertex planar graph is at most p4:5 n.
Based
on this result Dimitrios M. Thilikos connected the branchwidth with rradial
dominating
set which is another parameter in plane graphs. He proved that if a plane
graph has an rradial dominating set of size at most k, then the branchwidth of
the graph is at most r p4:5 k.
The purpose of this thesis is to provide a qualitative extension of this result.
What we show is that this upper bound is attained by a number of edges of a
spherecut decomposition, that is a linear function of k.gSpherecut decompositions , Dominating sets, Branchwidth, Protrusion decomposition, Radial distance1321292oMinimality and its Variations
20140408
( . ()Consider a firstorder structure S=(M,<,...) such that < is interpreted by a
dense linear order on M. S is called ominimal if and only if every firstorder
definable subset of M is a finite union of pointsets and intervals. A
firstorder theory T will be called ominimal if every model of T is an
ominimal structure. The notion of ominimality first presented at 80s (van
den Dries, Pillay and Steinhorn) and from then has been studied thoroughly by
many authors. In the first part of this work we present many properties of
these structures and theories which make them considered special. In the second
part we present some variations of ominimality and compare their properties.ominimality, Model theoryX, 91v9& z'!Q/)4.82E@:V~PsYSFd^kEfvq{ug{~"ƍ/
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