Heuristic algorithms for logical reasoning are increasingly successful on computationally difficult problems such as satisfiability, and these solvers enable applications from circuit verification to software synthesis. Whether a problem instance can be solved, however, often depends in practice on whether the correct solver was selected and its parameters appropriately set. Algorithm portfolios leverage past performance data to automatically select solvers likely to perform well on a given instance. Existing portfolio methods typically select only a single solver for each instance. This dissertation develops and evaluates a more general portfolio method, one that computes complete solver execution schedules, including repeated runs of nondeterministic algorithms, by explicitly incorporating probabilistic reasoning into its operation. This modular architecture for probabilistic portfolios (MAPP) includes novel solutions to three issues central to portfolio operation: first, it estimates solver performance distributions from limited data by constructing a generative model; second, it integrates domain-specific information by predicting instances on which solvers exhibit similar performance; and, third, it computes execution schedules using an efficient and effective dynamic programming approximation. In a series of empirical comparisons designed to replicate past solver competitions, MAPP outperforms the most prominent alternative portfolio methods. Its success validates a principled approach to portfolio operation, offers a tool for tackling difficult problems, and opens a path forward in algorithm portfolio design. / text

A data word (resp. a data tree) is a &#64257-nite word (resp. tree) whose every position carries a letter from a &#64257-nite alphabet and a datum form an in&#64257-nite domain. In this thesis we investigate automata and logics for data words and data trees with decidable reasoning problems: we focus on the emptiness problem in the case of automata, and the satis&#64257-ability problem in the case of logics. On data words, we present a decidable extension of the model of alternating register automata studied by Demri and Lazi'c. Further, we show the decidability of the satis&#64257-ability problem for the linear-time temporal logic on data words LTL_\downarrow (X, F, U) (studied by Demri and Lazi'c) with quanti&#64257-cation over data values. We also prove that the lower bounds of non-primitive recursiveness shown by Demri and Lazi'c for LTL&#8595- (X, F) carry over to LTL&#8595- (F). On data trees, we consider three decidable automata models with di&#64256-erent characteristics. We &#64257-rst introduce the Downward Data automaton (DD automata). Its execution consists in a transduction of the &#64257-nite labeling of the tree, and a veri&#64257-cation of data properties for every subtree of the transduced tree. This model is closed under boolean operations, but the tests it can make on the order of the siblings is very limited. Its emptiness problem is 2ExpTime. On the contrary, the other two automata models we introduce have an emptiness problem with a non-primitive recursive complexity, and are closed under intersection and union, but not complementation. They are both alternating automata with one register to store and compare data values. The automata class ATRA(guess, spread) extends the top-down automata ATRA of Jurdzinski and Lazic. We exhibit similar decidable extensions as the one showed in the case of data words. This class can test for any tree regular language--in contrast to DD automata. Finally, we consider a bottom-up alternating tree automaton with one register (called BUDA). Although the BUDA class is one-way, it has features that allow to test data properties by navigating the tree in both directions: upward and downward. In opposition to ATRA(guess, spread), this automaton cannot test for properties on the the sequence of siblings (like, for example, the order in which labels appear). All these three models have connections with the logic XPath--a logic conceived for xml documents, which can be seen as data trees. Through the aforementioned automata we show that the satis&#64257-ability of three natural fragments of XPath are decidable. These fragments are: downward XPath, where navigation can only be done by child and descendant axes- forward XPath, where navigation also contains the next sibling axis and its transitive closure- and vertical XPath, whose navigation consists in the child, descendant, parent and ancestor axes. Whereas downward XPath is ExpTime-complete, forward and vertical XPath have non-primitive recursive lower bounds.

Static program analysis is a core technology for both verifying and finding errors in programs but most static analyzers are complex pieces of software that are not without error. A Static analysis formalised as an abstract interpreter can be proved sound, however such proofs are significantly harder to do on the actual implementation of an analyser. To alleviate this problem we propose to generate Verification Conditions (VCs, formulae valid only if the results of the analyser are correct) and to discharge them using an Automated Theorem Prover (ATP). We generate formulae in Many-Sorted First-Order Logic (MSFOL), a logic that has been successfully used in deductive program verification. MSFOL is expressive enough to describe the results of complex analyses and to formalise the operational semantics of object-oriented languages. Using the same logic for both tasks allows us to prove the soundness of the VC generator using deductive verification tools. To ensure that VCs can be automatically discharged for complex analyses of the heap, we introduce a VC calculus that produces formulae belonging to a decidable fragment of MSFOL. Furthermore, to be able to certify different analyses with the same calculus, we describe a family of analyses with a parametric concretisation function and instrumentation of the semantics. To improve the reliability of ATPs, we also studied the result certification of Satisfiability Modulo Theory solvers, a family of ATPs dedicated to MSFOL. We propose a modular proof-system and a modular proof-verifier programmed and proved correct in Coq, that rely on exchangeable verifiers for each of the underlying theories.

In the last decade, Answer Set Programming (ASP) and Satisfiability (SAT) have been used to solve combinatorial search problems and practical applications in which they arise. In each of these formalisms, a tool called a solver is used to solve problems. A solver takes as input a specification of the problem – a logic program in the case of ASP, and a CNF theory for SAT – and produces as output a solution to the problem. Designing fast solvers is important for the success of this general-purpose approach to solving search problems. Classes of instances that pose challenges to solvers can help in this task. In this dissertation we create challenging yet simple benchmarks for existing solvers in ASP and SAT.We do so by providing models of simple logic programs as well as models of simple CNF theories. We then randomly generate logic programs as well as CNF theories from these models. Our experimental results show that computing answer sets of random logic programs as well as models of random CNF theories with carefully chosen parameters is hard for existing solvers. We generate random logic programs with 2-literals, and our experiments show that it is hard for ASP solvers to obtain answer sets of purely negative and constraint-free programs, indicating the importance of these programs in the development of ASP solvers. An easy-hard-easy pattern emerges as we compute the average number of choice points generated by ASP solvers on randomly generated 2-literal programs with an increasing number of rules. We provide an explanation for the emergence of this pattern in these programs. We also theoretically study the probability of existence of an answer set for sparse and dense 2-literal programs. We consider simple classes of mixed Horn formulas with purely positive 2- literal clauses and purely negated Horn clauses. First we consider a class of mixed Horn formulas wherein each formula has m 2-literal clauses and k-literal negated Horn clauses. We show that formulas that are generated from the phase transition region of this class are hard for complete SAT solvers. The second class of Mixed Horn Formulas we consider are obtained from completion of a certain class of random logic programs. We show the appearance of an easy-hard-easy pattern as we generate formulas from this class with increasing numbers of clauses, and that the formulas generated in the hard region can be used as benchmarks for testing incomplete SAT solvers.

This thesis investigates the use of local search methods in solving constraint problems. Such problems are very hard in general and local search offers a useful and successful alternative to existing techniques. The focus of the thesis is to analyze the techniques of invariants used in local search. The use of invariants have recently become the cornerstone of local search technology as they provide a declarative way to specify incremental algorithms. We have produced a series of program libraries in C++ known as the One-Way-Solver. The One-Way-Solver includes the implementation of incremental data structures and is a useful tool for the implementation of local search. The One-Way-Solver is applied to two challenging constraint problems, the Boolean Satisfiability Testing (SAT) and university course timetabling problems.

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

The thesis studies classes of Boolean formulae for which the well-known satisfiability problem is solvable in polynomially bounded time. It focusses on classes based on unit resolution; it describe classes of unit refutation complete formulae, unit propagation complete formulae and focuses on the class of SLUR formulae. It presents properties of SLUR formulae as well as the recently obtained results. The main result is the coNP-completness of membership testing. Finally, several hierarchies are built over the SLUR class and their properties and mutual relations are studied. Powered by TCPDF (www.tcpdf.org)

Un comportement distribué peut être décrit avec un multi-ensemble partiellement ordonné (pomset). Bien que compacts et très intuitifs, ces modèles sont difficiles à vérifier. La principale technique utilisée dans cette thèse est de ramener les problèmes de décision de la logique MSO sur les pomsets à des problèmes de décision sur les mots. Les problèmes considérés sont la satisfiabilité et la vérification. Le problème de la vérification pour une formule donnée et un pomset consiste à décider si une interprétation est vraie, et le problème de satisfiabilité consiste à décider si un pomset répondant à la formule existe. Le problème de satisfiabilité de MSO sur pomsets est indécidable. Une procédure de semi-décision peut apporter des solutions pour de nombreux cas, en dépit du fait qu'elle peut ne pas terminer. Nous proposons un nouveau modèle, que l'on appelle ⌈-Pomset, pouvant rendre l'exploration des pomsets possible. Par conséquent, si une formule est satisfiable alors notre approche mènera éventuellement à la détection d'une solution. De plus, en utilisant les ⌈-Pomsets comme modèles pour systèmes concurrents, le model-checking de formules ordre partiel sur systèmes concurrents est décidable. Certaines expérimentations ont été faites en utilisant l'outil MONA. Nous avons comparé aussi la puissance expressive de certains modèles classiques de la concurrence comme les traces de Mazurkiewicz avec les ⌈-Pomsets. / Multiset of partially ordered events (pomset) can describe distributed behavior. Although very intuitive and compact, these models are difficult to verify. The main technique used in this thesis is to bring back decision problems for MSO over pomsets to problems for MSO over words. The problems considered are satisfiability and verification. The verification problem for a formula and a given pomset consists in deciding whether such an interpretation exists, and the satisfiability problem consists in deciding whether a pomset satisfying the formula exists. The satisfiability problem of MSO over pomsets is undecidable. A semi-decision procedures can provide solutions for many cases despite the fact that they may not terminate. We propose a new model, so called ⌈-Pomset, making the exploration of pomsets space possible. Consequently, if a formula is satisfiable then our approach will eventually lead to the detection of a solution. Moreover, using ⌈-Pomsets as models for concurrent systems, the model checking of partial order formulas on concurrent systems is decidable. Some experiments have been made using MONA. We compare also the expressive power of some classical model of concurrency such as Mazurkiewicz traces with our ⌈-Pomsets.

abstract: Knowledge representation and reasoning is a prominent subject of study within the field of artificial intelligence that is concerned with the symbolic representation of knowledge in such a way to facilitate automated reasoning about this knowledge. Often in real-world domains, it is necessary to perform defeasible reasoning when representing default behaviors of systems. Answer Set Programming is a widely-used knowledge representation framework that is well-suited for such reasoning tasks and has been successfully applied to practical domains due to efficient computation through grounding--a process that replaces variables with variable-free terms--and propositional solvers similar to SAT solvers. However, some domains provide a challenge for grounding-based methods such as domains requiring reasoning about continuous time or resources. To address these domains, there have been several proposals to achieve efficiency through loose integrations with efficient declarative solvers such as constraint solvers or satisfiability modulo theories solvers. While these approaches successfully avoid substantial grounding, due to the loose integration, they are not suitable for performing defeasible reasoning on functions. As a result, this expressive reasoning on functions must either be performed using predicates to simulate the functions or in a way that is not elaboration tolerant. Neither compromise is reasonable; the former suffers from the grounding bottleneck when domains are large as is often the case in real-world domains while the latter necessitates encodings to be non-trivially modified for elaborations. This dissertation presents a novel framework called Answer Set Programming Modulo Theories (ASPMT) that is a tight integration of the stable model semantics and satisfiability modulo theories. This framework both supports defeasible reasoning about functions and alleviates the grounding bottleneck. Combining the strengths of Answer Set Programming and satisfiability modulo theories enables efficient continuous reasoning while still supporting rich reasoning features such as reasoning about defaults and reasoning in domains with incomplete knowledge. This framework is realized in two prototype implementations called MVSM and ASPMT2SMT, and the latter was recently incorporated into a non-monotonic spatial reasoning system. To define the semantics of this framework, we extend the first-order stable model semantics by Ferraris, Lee and Lifschitz to allow "intensional functions" and provide analyses of the theoretical properties of this new formalism and on the relationships between this and existing approaches. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2016

Submitted by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-02-07T17:47:31Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Mário A. P. Garcia.pdf: 1777955 bytes, checksum: bbc5f97c856505f518492e5c8ec65c28 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-02-07T17:47:47Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Mário A. P. Garcia.pdf: 1777955 bytes, checksum: bbc5f97c856505f518492e5c8ec65c28 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-02-07T17:48:08Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Mário A. P. Garcia.pdf: 1777955 bytes, checksum: bbc5f97c856505f518492e5c8ec65c28 (MD5) / Made available in DSpace on 2017-02-07T17:48:08Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Mário A. P. Garcia.pdf: 1777955 bytes, checksum: bbc5f97c856505f518492e5c8ec65c28 (MD5) Previous issue date: 2016-09-13 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The software development for embedded systems is getting faster and faster, which generally incurs an increase in the associated complexity. As a consequence, consumer electronics companies usually invest a lot of resources in fast and automatic verification mechanisms, in order to create robust systems and reduce product recall rates. In addition, further development-time reduction and system robustness can be achieved through cross-platform frameworks, such as Qt, which favor the reliable port of software stacks to different devices. Based on that, the present work proposes a simplified version of the Qt framework, which is integrated into a checker based on satisfiability modulo theories (SMT), name as the efficient SMT-based bounded model checker (ESBMC++), for verifying actual Qt-based applications, and presents a success rate of 89%, for the developed benchmark suite. We also evaluate our simplified version of the Qt framework using other state-of-the-art verifiers for C++ programs and an evaluation about their level of compliance. It is worth mentioning that the proposed methodology is the first one to formally verify Qt-based applications, which has the potential to devise new directions for software verification of portable code. / O desenvolvimento de software para sistemas embarcados tem crescido rapidamente, o que na maioria das vezes acarreta em um aumento da complexidade associada a esse tipo de projeto. Como consequência, as empresas de eletrônica de consumo costumam investir recursos em mecanismos de verificação rápida e automática, com o intuito de desenvolver sistemas robustos e assim reduzir as taxas de recall de produtos. Além disso, a redução no tempo de desenvolvimento e na robustez dos sistemas desenvolvidos podem ser alcançados através de frameworks multi-plataformas, tais como Qt, que oferece um conjunto de bibliotecas (gráficas) confiáveis para vários dispositivos embarcados. Desta forma, este trabalho propõe uma versão simplificada do framework Qt que integrado a um verificador baseado nas teorias do módulo da satisfatibilidade, denominado Efficient SMT-Based Bounded Model Checker (ESBMC++), verifica aplicações reais que ultilizam o Qt, apresentando uma taxa de sucesso de 89%, para os benchmarks desenvolvidos. Com a versão simplificada do framework Qt proposto, também foi feita uma avaliação ultilizando outros verificadores que se encontram no estado da arte para verificação de programas em C++ e uma avalição a cerca de seu nível de conformidade. Dessa maneira, a metodologia proposta se afirma como a primeira a verificar formalmente aplicações baseadas no framework Qt, além de possuir um potencial para desenvolver novas frentes para a verificação de código portátil.