No description available.

Many problems in nature can be represented as some kind of a satisfiability problem. Several SAT solvers and SMT solvers have been developed in the last decade with the goal of checking the satisfiability of different SAT problems. An all-solution satisfiability modulo theories on top of the Z3 SMT solver is presented that uses the clause blocking algorithm to find all the solution sets of a SAT problem. Then, an incremental All-SMT solver has been presented based on the all-SMT solver which is able to find the satisfiable answers of an incremental SMT problem based on the solution set of the original problem.

Η παρούσα διπλωµατική εργασία ασχολείται με το θέμα των Αλγορίθμων Επίλυσης Προβληµάτων SAT. Η εργασία αυτή εκπονήθηκε στα πλαίσια του Εργαστηρίου Ενσύρµατης Επικοινωνίας του Τµήματος Ηλεκτρολόγων Μηχανικών και Τεχνολογίας Υπολογιστών της Πολυτεχνικής Σχολής του Πανεπιστηµίου Πατρών. Σκοπός της είναι η δημιουργία ενός Προσομοιωτή των αλγορίθμων αυτών, ο οποίος να μπορεί να προσπελαστεί από οποιονδήποτε μέσω του διαδικτύου. Αρχικά έγινε µία εισαγωγή στο αντικείμενο της Τεχνητής Νοημοσύνης και πιο συγκεκριµένα στην Προτασιακή Λογική, ενώ δόθηκε και το απαραίτητο υπόβαθρο για να κατανοηθεί το πρόβληµμα και οι τεχνικές λύσης του. Τέλος, επιλέχθηκε να γίνει η υλοποίηση του Προσωμοιωτή σε Java. / This diploma dissertation deals with SAT solvers, algorithms for the Boolean satisfiability problem. It was produced in the Wire Communications Laboratory of the Electrical and Computer Engineering Department of the University of Patras. Its aim is to create a simulator for these algorithms, accessible to anyone via the Internet. An introduction to the field of Artificial Intelligence and more specifically to Propositional Calculus was given as well as the necessary groundwork to understand the problem and its solution approaches. The simulation implementation was developed in Java

Diese Arbeit befasst sich mit Worst-Case-Algorithmen für das Erfüllbarkeitsproblem boolescher Ausdrücke in konjunktiver Normalform. Im Wesentlichen betrachten wir Laufzeitschranken drei verschiedener Algorithmen, zwei für 3-SAT und einen für Unique-k-SAT. Wir entwickeln einen randomisierten Algorithmus, der eine Lösung eines erfüllbaren 3-KNF-Ausdrucks G mit n Variablen mit einer erwarteten Laufzeit von O(1.32793^n) findet. Der Algorithmus basiert auf der Analyse sogenannter Strings, welche Sequenzen von Klauseln der Länge drei sind. Dabei dürfen einerseits nicht aufeinanderfolgende Klauseln keine Variablen und andererseits aufeinanderfolgende Klauseln ein oder zwei Variablen gemeinsam haben. Gibt es wenige Strings, so treffen wir wahrscheinlich bereits während der String-Suche auf eine Lösung von G. 1999 entwarf Schöning einen Algorithmus mit einer Schranke von O(1.3334^n) für 3-SAT. Viele Strings erlauben es, die Laufzeit dieses Algorithmusses zu verbessern. Weiterhin werden wir den PPSZ-Algorithmus für Unique-k-SAT derandomisieren. Der 1998 von Paturi, Pudlak, Saks und Zane vorgestellte PPSZ-Algorithmus hat die besondere Eigenschaft, dass die Lösung eines eindeutig erfüllbaren 3-KNF-Ausdrucks in höchstens O(1.3071^n) erwarteter Laufzeit gefunden wird. Die derandomisierte Variante des Algorithmusses für Unique-k-SAT hat im Wesentlichen die gleiche Laufzeitschranke. Wir erreichen damit die momentan beste deterministische Worst-Case-Schranke für Unique-k-SAT. Zur Derandomisierung wenden wir die "Methode der kleinen Zufallsräume" an. Schließlich verbessern wir die Schranke für den Algorithmus von Iwama und Tamaki. 2003 kombinierten Iwama und Tamaki den PPSZ-Algorithmus mit Schönigs Algorithmus und konnten eine Schranke von O(1.3238^n) bewiesen. Um seinen Beitrag zum kombinierten Algorithmus zu steigern, justieren wir die Schranke des PPSZ-Algorithmusses. Damit erhalten wir die momentan beste randomisierte Worst-Case-Schranke für das 3-SAT-Problem von O(1.32216^n). / This work deals with worst-case algorithms for the satisfiability problem regarding boolean formulas in conjunctive normal form. The main part of this work consists of the analysis of the running time of three different algorithms, two for 3-SAT and one for Unique-k-SAT. We establish a randomized algorithm that finds a satisfying assignment for a satisfiable 3-CNF formula G on n variables in O(1.32793^n) expected running time. The algorithm is based on the analysis of so-called strings, which are sequences of clauses of size three, whereby non-succeeding clauses do not share a variable, and succeeding clauses share one or two variables. If there are not many strings, it is likely that we already encounter a solution of G while searching for strings. In 1999, Schöning proved a bound of O(1.3334^n) for 3-SAT. If there are many strings, we use them to improve the running time of Schöning''s algorithm. Furthermore, we derandomize the PPSZ algorithm for Unique-k-SAT. The PPSZ algorithm presented by Paturi, Pudlak, Saks, and Zane in 1998 has the feature that the solution of a uniquely satisfiable 3-CNF formula can be found in expected running time at most O(1.3071^n). In general, we will obtain a derandomized version of the algorithm for Unique-k-SAT that has essentially the same bound as the randomized version. This settles the currently best known deterministic worst-case bound for the Unique-k-SAT problem. We apply the `Method of Small Sample Spaces'' in order to derandomize the algorithm. Finally, we improve the bound for the algorithm of Iwama and Tamaki to get the currently best known randomized worst-case bound for the 3-SAT problem of O(1.32216^n). In 2003 Iwama and Tamaki combined Schöning''s and the PPSZ algorithm to yield an O(1.3238^n) bound. We tweak the bound for the PPSZ algorithm to get a slightly better contribution to the combined algorithm.

Στην εργασία αυτή ασχοληθήκαμε με το πρόβλημα της Πιθανοτικής Ικανοποιησιμότητας. Παρουσιάσαμε ανάλυση της πολυπλοκότητας του προβλήματος και το επιλύσαμε με την βοήθεια του λογισμικού πακέτου CPLEX. Περιγράψαμε προσεγγιστικούς αλγόριθμους για το πρόβλημα της Μέγιστης Ικανοποιησιμότητας που χρησιμοποιείται στην διαδικασία της Column Generation. Τέλος, πριγράψαμε το αντίστροφο πρόβλημα των συχνών στοιχειοσυνόλων και την σχέση του με το πρόβλημα της Μέγιστης Ικανοποιησιμότητας. / This thesis is about the problem of probabilistic satisfiability. We describe its computational complexity, we solve the problem using CPLEX, we discribe some approximations on Maximum Satisfiability. Finally, we describe the connection between the problem of Probabilistic Satisfiability and the inverse frequent itemset mining.

This thesis is divided into two parts. In the first part we describe a new Monte Carlo algorithm for the consistent and unbiased estimation of multidimensional integrals and the efficient sampling from multidimensional densities. The algorithm is inspired by the classical splitting method and can be applied to general static simulation models. We provide examples from rare-event probability estimation, counting, optimization, and sampling, demonstrating that the proposed method can outperform existing Markov chain sampling methods in terms of convergence speed and accuracy. In the second part we present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability.

No / This paper proposes an approximate optimization approach, called QEAM, which combines a P system with active membranes and a quantum-inspired evolutionary algorithm. QEAM uses the hierarchical arrangement of the compartments and developmental rules of a P system with active membranes, and the objects consisting of quantum-inspired bit individuals, a probabilistic observation and the evolutionary rules designed with quantum-inspired gates to specify the membrane algorithms. A large number of experiments carried out on benchmark instances of satisfiability problem show that QEAM outperforms QEPS (quantum-inspired evolutionary algorithm based on P systems) and its counterpart quantum-inspired evolutionary algorithm.

<p>The Ph.D. thesis addresses a comprehensive study of the bee colony<br />optimization meta-heuristic method (BCO). Theoretical analysis of the<br />method is conducted with the tools of probability theory. Necessary and<br />sufficient conditions are presented that establish convergence of the BCO<br />method towards an optimal solution. Three parallelization strategies and five<br />corresponding implementations are proposed for BCO for distributed-memory<br />systems. The influence of method&rsquo;s parameters on the performance of the<br />BCO algorithm for two combinatorial optimization problems is analyzed<br />through the experimental study.</p> / <p>Докторска дисертације се бави испитивањем метахеуристичке методе<br />оптимизације колонијом пчела. Извршена је теоријска анализа<br />асимптотске конвергенције методе посматрањем конвергенције низа<br />случајних променљивих. Установљени су довољни и потребни услови<br />за које метода конвергира ка оптималном решењу. Предложене су три<br />стратегије паралелизације и пет одговарајућих имплементација конст-<br />руктивне варијанте методе за рачунаре са дистрибуираном меморијом.<br />Извршено је експериментално испитивање утицаја параметара методе<br />на њене перформансе за два различита комбинаторна проблема:<br />проблем распоређивања и проблем задовољивости.</p> / <p>Doktorska disertacije se bavi ispitivanjem metaheurističke metode<br />optimizacije kolonijom pčela. Izvršena je teorijska analiza<br />asimptotske konvergencije metode posmatranjem konvergencije niza<br />slučajnih promenljivih. Ustanovljeni su dovoljni i potrebni uslovi<br />za koje metoda konvergira ka optimalnom rešenju. Predložene su tri<br />strategije paralelizacije i pet odgovarajućih implementacija konst-<br />ruktivne varijante metode za računare sa distribuiranom memorijom.<br />Izvršeno je eksperimentalno ispitivanje uticaja parametara metode<br />na njene performanse za dva različita kombinatorna problema:<br />problem raspoređivanja i problem zadovoljivosti.</p>

Le raisonnement spatial et temporel qualitatif est un domaine principal d’études de l’intelligence artificielle et, en particulier, du domaine de la représentation des connaissances, qui traite des concepts cognitifs fondamentaux de l’espace et du temps de manière abstraite. Dans notre thèse, nous nous focalisons sur les formalismes du domaine du raisonnement spatial et temporel qualitatif représentant les informations par des contraintes et apportons des contributions sur plusieurs aspects. En particulier, étant donnée des bases de connaissances d’informations qualitatives sur l’espace ou le temps, nous définissons des nouvelles conditions de consistance locale et des techniques associées afin de résoudre efficacement les problèmes fondamentaux se posant. Nous traitons notamment du problème de la satisfiabilité qui est le problème de décider s’il existe une interprétation quantitative de toutes les entités satisfaisant l’ensemble des contraintes qualitatives. Nous considérons également le problème de l’étiquetage minimal qui consiste à déterminer pour toutes les contraintes qualitatives les relations de base participant à au moins une solution ainsi que le problème de redondance consistant à déterminer les contraintes qualitatives non redondantes. En outre, nous enrichissons le domaine des formalismes spatio-temporels par des contributions concernant une logique spatio-temporelle combinant la logique temporelle propositionnelle (PTL) avec un langage de contraintes qualitatives spatiales et une étude de la problématique consistant à gérer une séquence temporelle de configurations spatiales qualitatives devant satisfaire des contraintes de transition. / Qualitative Spatial and Temporal Reasoning is a major field of study in Artificial Intelligence and, particularly, in Knowledge Representation, which deals with the fundamental cognitive concepts of space and time in an abstract manner. In our thesis, we focus on qualitative constraint-based spatial and temporal formalisms and make contributions to several aspects. In particular, given a knowledge base of qualitative spatial or temporal information, we define novel local consistency conditions and related techniques to efficiently solve the fundamental reasoning problems that are associated with such knowledge bases. These reasoning problems consist of the satisfiability problem, which is the problem of deciding whether there exists a quantitative interpretation of all the entities of a knowledge base such that all of its qualitative relations are satisfied by that interpretation, the minimal labeling problem, which is the problem of determining all the atoms for each of the qualitative relations of a knowledge base that participate in at least one of its solutions, and the redundancy problem, which is the problem of obtaining all the non-redundant qualitative relations of a knowledge base. Further, we enrich the field of spatio-temporal formalisms that combine space and time in an interrelated manner by making contributions with respect to a qualitative spatio-temporal logic that results by combining the propositional temporal logic (PTL) with a qualitative spatial constraint language, and by investigating the task of ordering a temporal sequence of qualitative spatial configurations to meet certain transition constraints.

Nondeterministic finite automaton is an important tool, which is used to process strings in many different areas of programming. It is important to try to reduce its size for increasing programs' effectiveness. However, this problem is computationally hard, so we need to search for new techniques. Basics of finite automata are described in this work. Some methods for their reduction are then introduced. Usable reduction algorithms are described in greater detail. Then they are implemented and tested. The test results are finally evaluated.