Effective Auxiliary Variables via Structured Reencoding

Extended resolution shows that auxiliary variables are very powerful in theory. However, attempts to exploit this potential in practice have had limited success. One reasonably effective method in this regard is bounded variable addition (BVA), which automatically reencodes formulas by introducing new variables and eliminating clauses, often significantly reducing formula size. We find motivating examples suggesting that the performance improvement caused by BVA stems not only from this size reduction but also from the introduction of effective auxiliary variables. Analyzing specific packing-coloring instances, we discover that BVA is fragile with respect to formula randomization, relying on variable order to break ties. With this understanding, we augment BVA with a heuristic for breaking ties in a structured way. We evaluate our new preprocessing technique, Structured BVA (SBVA), on more than 29 000 formulas from previous SAT competitions and show that it is robust to randomization. In a simulated competition setting, our implementation outperforms BVA on both randomized and original formulas, and appears to be well-suited for certain families of formulas

Finding Unsatisfiable Subformulas with Stochastic Method

Abstract. Explaining the causes of infeasibility of Boolean formulas has many practical applications in various fields. A small unsatisfiable subformula provides a succinct explanation of infeasibility and is valuable for applications. In recent years the problem of finding unsatisfiable subformulas has been addressed frequently by research works, which are mostly based on the SAT solvers with DPLL backtrack-search algorithm. However little attention has been concentrated on extraction of unsatisfiable subformulas using stochastic methods. In this paper, we propose a resolution-based stochastic local search algorithm to derive unsatisfiable subformulas. This approach directly constructs the resolution sequences for proving unsatisfiability with a local search procedure, and then extracts small unsatisfiable subformulas from the refutation traces. We report and analyze the experimental results on benchmarks

Synthesis of FPGA-based accelerators implementing recursive algorithms

Doutoramento em Engenharia InformáticaO desenvolvimento de sistemas computacionais é um processo complexo, com múltiplas etapas, que requer uma análise profunda do problema, levando em consideração as limitações e os requisitos aplicáveis. Tal tarefa envolve a exploração de técnicas alternativas e de algoritmos computacionais para optimizar o sistema e satisfazer os requisitos estabelecidos. Neste contexto, uma das mais importantes etapas é a análise e implementação de algoritmos computacionais. Enormes avanços tecnológicos no âmbito das FPGAs (Field-Programmable Gate Arrays) tornaram possível o desenvolvimento de sistemas de engenharia extremamente complexos. Contudo, o número de transístores disponíveis por chip está a crescer mais rapidamente do que a capacidade que temos para desenvolver sistemas que tirem proveito desse crescimento. Esta limitação já bem conhecida, antes de se revelar com FPGAs, já se verificava com ASICs (Application-Specific Integrated Circuits) e tem vindo a aumentar continuamente. O desenvolvimento de sistemas com base em FPGAs de alta capacidade envolve uma grande variedade de ferramentas, incluindo métodos para a implementação eficiente de algoritmos computacionais. Esta tese pretende proporcionar uma contribuição nesta área, tirando partido da reutilização, do aumento do nível de abstracção e de especificações algorítmicas mais automatizadas e claras. Mais especificamente, é apresentado um estudo que foi levado a cabo no sentido de obter critérios relativos à implementação em hardware de algoritmos recursivos versus iterativos. Depois de serem apresentadas algumas das estratégias para implementar recursividade em hardware mais significativas, descreve-se, em pormenor, um conjunto de algoritmos para resolver problemas de pesquisa combinatória (considerados enquanto exemplos de aplicação). Versões recursivas e iterativas destes algoritmos foram implementados e testados em FPGA. Com base nos resultados obtidos, é feita uma cuidada análise comparativa. Novas ferramentas e técnicas de investigação que foram desenvolvidas no âmbito desta tese são também discutidas e demonstradas.Design of computational systems is a complex multistage process which requires a deep analysis of the problem, taking into account relevant limitations and constraints as well as software/hardware co-design. Such task involves exploring competitive techniques and computational algorithms, enabling the system to be optimized while satisfying given requirements. In this context, one of the most important stages is analysis and implementation of computational algorithms. Tremendous progress in the scope of FPGA (Field-Programmable Gate Array) technology has made it possible to design very complicated engineering systems. However, the number of available transistors grows faster than the ability to meaningfully design with them. This situation is a well known design productivity gap, which was inherited by FPGA from ASIC (Application-Specific Integrated Circuit) and which is increasing continuously. Developing engineering systems on the basis of high capacity FPGAs involves a wide variety of design tools, including methods for efficient implementation of computational algorithms. The thesis is intended to provide a contribution in this area by aiming at reuse, high level abstraction, automation, and clearness of algorithmic specifications. More specifically, it presents research studies which have been carried out in order to obtain criteria regarding implementation of recursive vs. iterative algorithms in hardware. After describing some of the most relevant strategies for implementing recursion in hardware, a selection of algorithms for solving combinatorial search problems (considered as application examples) are also described in detail. Iterative and recursive versions of these algorithms have been implemented and tested in FPGA. Taking into consideration the results obtained, a careful comparative analysis is given. New research-oriented tools and techniques for hardware design which have been developed in the scope of this thesis are also discussed and demonstrated

Architecture FPGA améliorée et flot de conception pour une reconfiguration matérielle en ligne efficace

The self-reconfiguration capabilities of modern FPGA architectures pave the way for dynamic applications able to adapt to transient events. The CAD flows of modern architectures are nowadays mature but limited by the constraints induced by the complexity of FPGA circuits. In this thesis, multiple contributions are developed to propose an FPGA architecture supporting the dynamic placement of hardware tasks. First, an intermediate representation of these tasks configuration data, independent from their final position, is presented. This representation allows to compress the task data up to 11x with regard to its conventional raw counterpart. An accompanying CAD flow, based on state-of-the-art tools, is proposed to generate relocatable tasks from a high-level description. Then, the online behavior of this mechanism is studied. Two algorithms allowing to decode and create in real-time the conventional bit-stream are described. In addition, an enhancement of the FPGA interconnection network is proposedto increase the placement flexibility of heterogeneous tasks, at the cost of a 10% increase in average of the critical path delay. Eventually, a configurable substitute to the configuration memory found in FPGAs is studied to ease their partial reconfiguration.Les capacités d'auto-reconfiguration des architectures FPGA modernes ouvrent la voie à des applications dynamiques capables d'adapter leur fonctionnement pour répondre à des évènements ponctuels. Les flots de reconfiguration des architectures commerciales sont aujourd'hui aboutis mais limités par des contraintes inhérentes à la complexité de ces circuits. Dans cette thèse, plusieurs contributions sont avancées afin de proposer une architecture FPGA reconfigurable permettant le placement dynamique de tâches matérielles. Dans un premier temps, une représentation intermédiaire des données de configuration de ces tâches, indépendante de leur positionnement final, est présentée. Cette représentation permet notamment d'atteindre des taux de compression allant jusqu'à 11x par rapport à la représentation brute d'une tâche. Un flot de conception basé sur des outils de l'état de l'art accompagne cette représentation et génère des tâches relogeables à partir d'une description haut-niveau. Ensuite, le comportement en ligne de ce mécanisme est étudié. Deux algorithmes permettant le décodage de ces tâches et la génération en temps-réel des données de configuration propres à l'architectures son décrits. Par ailleurs, une amélioration du réseau d'interconnexion d'une architecture FPGA est proposée pour accroître la flexibilité du placement de tâches hétérogènes, avec une augmentation de 10% en moyenne du délai du chemin critique. Enfin, une alternative programmable aux mémoires de configuration de ces circuits est étudiée pour faciliter leur reconfiguration partielle