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)

AN ABSTRACT OF THE DISSERTATION OF PRAGYAN P. MOHANTY, for the Doctor of Philosophy degree in ELECTRICAL AND COMPUTER ENGINEERING, presented on June 11, 2015, at Southern Illinois University Carbondale. TITLE: FUNCTION-BASED ALGORITHMS FOR BIOLOGICAL SEQUENCES MAJOR PROFESSOR: Dr. Spyros Tragoudas Two problems at two different abstraction levels of computational biology are studied. At the molecular level, efficient pattern matching algorithms in DNA sequences are presented. For gene order data, an efficient data structure is presented capable of storing all gene re-orderings in a systematic manner. A common characteristic of presented methods is the use of binary decision diagrams that store and manipulate binary functions. Searching for a particular pattern in a very large DNA database, is a fundamental and essential component in computational biology. In the biological world, pattern matching is required for finding repeats in a particular DNA sequence, finding motif and aligning sequences etc. Due to immense amount and continuous increase of biological data, the searching process requires very fast algorithms. This also requires encoding schemes for efficient storage of these search processes to operate on. Due to continuous progress in genome sequencing, genome rearrangements and construction of evolutionary genome graphs, which represent the relationships between genomes, become challenging tasks. Previous approaches are largely based on distance measure so that relationship between more phylogenetic species can be established with some specifically required rearrangement operations and hence within certain computational time. However because of the large volume of the available data, storage space and construction time for this evolutionary graph is still a problem. In addition, it is important to keep track of all possible rearrangement operations for a particular genome as biological processes are uncertain. This study presents a binary function-based tool set for efficient DNA sequence storage. A novel scalable method is also developed for fast offline pattern searches in large DNA sequences. This study also presents a method which efficiently stores all the gene sequences associated with all possible genome rearrangements such as transpositions and construct the evolutionary genome structure much faster for multiple species. The developed methods benefit from the use of Boolean functions; their compact storage using canonical data structure and the existence of built-in operators for these data structures. The time complexities depend on the size of the data structures used for storing the functions that represent the DNA sequences and/or gene sequences. It is shown that the presented approaches exhibit sub linear time complexity to the sequence size. The number of nodes present in the DNA data structure, string search time on these data structures, depths of the genome graph structure, and the time of the rearrangement operations are reported. Experiments on DNA sequences from the NCBI database are conducted for DNA sequence storage and search process. Experiments on large gene order data sets such as: human mitochondrial data and plant chloroplast data are conducted and depth of this structure was studied for evolutionary processes on gene sequences. The results show that the developed approaches are scalable.

abstract: Biological systems are complex in many dimensions as endless transportation and communication networks all function simultaneously. Our ability to intervene within both healthy and diseased systems is tied directly to our ability to understand and model core functionality. The progress in increasingly accurate and thorough high-throughput measurement technologies has provided a deluge of data from which we may attempt to infer a representation of the true genetic regulatory system. A gene regulatory network model, if accurate enough, may allow us to perform hypothesis testing in the form of computational experiments. Of great importance to modeling accuracy is the acknowledgment of biological contexts within the models -- i.e. recognizing the heterogeneous nature of the true biological system and the data it generates. This marriage of engineering, mathematics and computer science with systems biology creates a cycle of progress between computer simulation and lab experimentation, rapidly translating interventions and treatments for patients from the bench to the bedside. This dissertation will first discuss the landscape for modeling the biological system, explore the identification of targets for intervention in Boolean network models of biological interactions, and explore context specificity both in new graphical depictions of models embodying context-specific genomic regulation and in novel analysis approaches designed to reveal embedded contextual information. Overall, the dissertation will explore a spectrum of biological modeling with a goal towards therapeutic intervention, with both formal and informal notions of biological context, in such a way that will enable future work to have an even greater impact in terms of direct patient benefit on an individualized level. / Dissertation/Thesis / Ph.D. Computer Science 2013

Em sistemas biológicos, o estudo da estabilidade das redes de regulação gênica é visto como uma contribuição importante que a Matemática pode proporcionar a pesquisas sobre câncer e outras doenças genéticas. Neste trabalho, utilizamos o conceito de ``canalização\'\' como sinônimo de estabilidade em uma rede biológica. Como as características de uma rede de regulação canalizada ainda são superficialmente compreendidas, estudamos esse conceito sob o ponto de vista computacional: propomos um modelo matemático simplificado para descrever o fenômeno e realizamos algumas análises sobre o mesmo. Mais especificamente, a estabilidade da maior bacia de atração das redes Booleanas - um clássico paradigma para a modelagem de redes de regulação - é analisada. Os resultados indicam que a estabilidade da maior bacia de atração está relacionada com dados biológicos sobre o crescimento de colônias de leveduras e que considerações sobre a interação entre as funções Booleanas e a topologia da rede devem ser realizadas conjuntamente na análise de redes estáveis. / In biological systems, the study of gene regulatory networks stability is seen as an important contribution that Mathematics can make to cancer research and that of other genetic diseases. In this work, we consider the concept of ``canalization\'\' as a consequence of stability in gene regulatory networks. The characteristics of canalized regulatory networks are superficially understood. Hence, we study the canalization concept under a computational framework: a simplified model is proposed to describe the phenomenon using Boolean Networks - a classical paradigm to modeling regulatory networks. Specifically, the stability of the largest basin of attraction in gene regulatory networks is analyzed. Our results indicate that the stability of the largest basin of attraction is related to biological data on growth of yeast colonies, and that thoughts about the interaction between Boolean functions and network topologies must be given in the analysis of stable networks.

Quadratic optimization problems arise in various real world application domains including engineering design, microeconomics, genetic algorithms, integrated circuit chip design, probabilistic graphical models and computer vision. In particular, there are many problems in computer vision that require binary quadratic optimization such as motion segmentation, correspondences, figure-ground segmentation, clustering, grouping, subgraph matching, and digital matting. The objective of an optimization algorithm can be related to the state of a physical system, where the goal is to bring the initial arbitrary state of the system to a state with minimum possible energy. By recognizing that the Hamiltonian of nanomagnets can be expressed in a quadratic form, we exploit the energy minimization aspect of these nanomagnets to solve the quadratic optimization problem in a direct manner. Most hard problems especially in computer vision can be naturally cast as energy minimization problems and solving these using traditional techniques like simulated annealing, graph cuts evidently associate with exorbitant computational efforts. In this dissertation, transcoding the conceptual crossover between the magnetic Hamiltonian and the optimization problem, we envision a nanomagnetic coprocessor with a grid of nanomagnets embracing an optimization heuristic enabling to solve energy minimization in a single clock cycle. We will essentially be solving an optimization problem with each input-and-readout cycle as compared to orders of magnitude more clock cycles that would be needed in a Boolean logic circuit. The dissertation presents results for quadratic minimization problem in the context of perceptual organization of edges in computer vision and compare quality of results using traditional optimization methods and that expected from magnetic computing. The dissertation also presents image processing algorithms for analysis of results produced by actual fabrication of the magnetic systems.

L’analyse de groupes de données binaires est aujourd’hui un défi au vu des quantités de données collectées. Elle peut être réalisée par des approches logiques. Ces approches identifient dessous-ensembles d’attributs booléens pertinents pour caractériser les observations d’un groupe et peuvent aider l’utilisateur à mieux comprendre les propriétés de ce groupe.Cette thèse présente une approche pour caractériser des groupes de données binaires en identifiant un sous-ensemble minimal d’attributs permettant de distinguer les données de différents groupes.Nous avons défini avec précision le problème de la caractérisation multiple et proposé de nouveaux algorithmes qui peuvent être utilisés pour résoudre ses différentes variantes. Notre approche de caractérisation de données peut être étendue à la recherche de patterns (motifs) dans le cadre de l’analyse logique de données. Un pattern peut être considéré comme une explication partielle des observations positives pouvant être utilisées par les praticiens, par exemple à des fins de diagnostic. De nombreux patterns existent et plusieurs critères de préférence peuvent être ajoutés pour se concentrer sur des ensembles plus restreints (prime patterns,strong patterns,. . .). Nous proposons donc une comparaison entre ces deux méthodologies ainsi que des algorithmes pour générer des patterns. Un autre objectif est d’étudier les propriétés des solutions calculées en fonction des propriétés topologiques des instances. Des expériences sont menées sur de véritables ensembles de données biologiques. / Analysis of groups of binary data is now a challenge given the amount of collected data. It can be achieved by logical based approaches. These approaches identify subsets of relevant Boolean attributes to characterize the observations of a group and may help the user to better understand the properties of this group. This thesis presents an approach for characterizing groups of binary data by identifying a minimal subset of attributes that allows to distinguish data from different groups. We have precisely defined the multiple characterization problem and proposed new algorithms that can be used to solve its different variants. Our data characterization approach can be extended to search for patterns in the framework of logical analysis of data. A pattern can be considered as a partial explanation of the positive observations that can be used by practitioners, for instance for diagnosis purposes. Many patterns may exist and several preference criteria can be added in order to focus on more restricted sets of patterns (prime patterns, strong patterns, . . . ). We propose a comparison between these two methodologies as well as algorithms for generating patterns. The purpose is also to precisely study the properties of the solutions that are computed with regards to the topological properties of the instances. Experiments are thus conducted on real biological data.

The open problem in knowledge compilation of whether the language PI is at least as succinct as MODS is answered in the negative. For this purpose a class of Boolean functions with a number of prime implicants that is superpolynomial in their number of false points is constructed. A lower bound (proving that PI is not at least as succinct as MODS), an upper bound (proving that the counterexample cannot yield an exponential separation of PI and MODS) and the precise number of the prime implicants of these functions is computed. Powered by TCPDF (www.tcpdf.org)

Le chiffrement complètement homomorphe est une classe de chiffrement permettant de calculer n’importe quelle fonction sur des données chiffrées et de produire une version chiffrée du résultat. Il permet de déléguer des données à un cloud de façon sécurisée, faire effectuer des calculs, tout en gardant le caractère privé de ces données. Cependant, l’innéficacité actuelle des schémas de chiffrement complètement homomorphes, et leur inadéquation au contexte de délégation de calculs, rend son usage seul insuffisant pour cette application. Ces deux problèmes peuvent être résolus, en utilisant ce chiffrement dans un cadre plus large, en le combinant avec un schéma de chiffrement symétrique. Cette combinaison donne naissance au chiffrement complètement homomorphe hybride, conçu dans le but d’une délégation de calculs efficace, garantissant des notions de sécurité et de vie privée. Dans cette thèse, nous étudions le chiffrement complètement homomorphe hybride et ses composantes, à travers la conception de primitives cryptographiques symétriques rendant efficace cette construction hybride. En examinant les schémas de chiffrement complètement homomorphes, nous developpons des outils pour utiliser efficacement leurs propriétés homomorphiques dans un cadre plus complexe. En analysant différents schémas symétriques, et leurs composantes, nous déterminons de bons candidats pour le contexte hybride. En étudiant la sécurité des constructions optimisant l’évaluation homomorphique, nous contribuons au domaine des fonctions booléennes utilisées en cryptologie. Plus particulièrement, nous introduisons une nouvelle famille de schémas de chiffrement symétriques, avec une nouvelle construction, adaptée au contexte hybride. Ensuite, nous nous intéressons à son comportement homomorphique, et nous étudions la sécurité de cette construction. Finalement, les particularités de cette famille de schémas de chiffrement motivant des cryptanalyses spécifiques, nous développons et analysons de nouveaux critères cryptographiques booléens. / Fully homomorphic encryption, firstly built in 2009, is a very powerful kind of encryption, allowing to compute any function on encrypted data, and to get an encrypted version of the result. Such encryption enables to securely delegate data to a cloud, ask for computations, recover the result, while keeping private the data during the whole process. However, today’s inefficiency of fully homomorphic encryption, and its inadequateness to the outsourcing computation context, makes its use alone insufficient for this application. Both of these issues can be circumvented, using fully homomorphic encryption in a larger framework, by combining it with a symmetric encryption scheme. This combination gives a hybrid fully homomorphic framework, designed towards efficient outsourcing computation, providing both security and privacy. In this thesis, we contribute to the study of hybridfully homomorphic framework, through the analysis, and the design of symmetric primitives making efficient this hybrid construction. Through the examination of fully homomorphic encryption schemes, we develop tools to efficiently use the homomorphic properties in a more complex framework. By investigating various symmetric encryption schemes, and buildingblocks up to the circuit level, we determine good candidates for a hybrid context. Through evaluating the security of constructions optimizing the homomorphic evaluation, we contribute to a wide study within the cryptographic Boolean functions area. More particularly, we introduce a new family of symmetric encryption schemes, with a new design, adapted to the hybrid fully homomorphic framework. We then investigate its behavior relatively to homomorphic evaluation, and we address the security of such design. Finally, particularities of this family of ciphers motivate specific cryptanalyses, therefore we develop and analyze new cryptographic Boolean criteria.

The aim of this work is to create a library for Boolean operations on 3D polygonal meshes. Resulting library has to support open models, its memory requirements shouldn't exceed those of existing solutions and it should, ideally, support multiple models. Most of the existing solutions are vulnerable to arithmetic inaccuracies, or do not support open meshes. The solution is based on Adaptive Mesh Booleans method which treats input models as adaptive surfaces. This method assumes that input models can be arbitrarily refined and no individual polygon is particularly important. Instead of computing exact polygon intersections, the input meshes are refined in intersection regions, intersecting polygons are discarded and created holes are closed. Advantages of this approach are robustness against numerical errors, support for open meshes, possibility to trade accuracy for computation time and ability to solve cases like co-planar and near-coincident regions. The resulting library offers three Boolean operations: union, difference and intersection.