Catálogo de publicaciones - libros

We give a randomized algorithm for testing satisfiability of Boolean formulas in conjunctive normal form with no restriction on clause length. Its running time is at most 2 up to a polynomial factor, where = ln (/) + (ln ln ) and , are respectively the number of variables and the number of clauses in the input formula. This bound is asymptotically better than the previously best known 2 bound for SAT.

Current algorithms for bounded model checking (BMC) use SAT methods for checking satisfiability of Boolean formulas. These BMC methods suffer from a potential memory explosion problem. Methods based on the validity of Quantified Boolean Formulas (QBF) allow an exponentially more succinct representation of the checked formulas, but have not been widely used, because of the lack of an efficient decision procedure for QBF. We evaluate the usage of QBF in BMC, using general-purpose SAT and QBF solvers. We also present a special-purpose decision procedure for QBF used in BMC, and compare our technique with the methods using general-purpose SAT and QBF solvers on real-life industrial benchmarks. Our procedure performs much better for BMC than the general-purpose QBF solvers, without incurring the space overhead of propositional SAT.

This paper presents a new technique to derive an initial static variable ordering for efficient SAT search. Our approach not only exploits variable activity and connectivity information simultaneously, but it also analyzes how tightly the variables are related to each other. For this purpose, a new metric is proposed – the degree of correlation among pairs of variables. Variable activity and correlation information is modeled (implicitly) as a weighted graph. A topological analysis of this graph generates an order for SAT search. Also, the effect of decision-assignments on clause-variable dependencies is taken into account during this analysis. An algorithm called ACCORD (ACtivity – CORrelation – ORDering) is proposed for this purpose. Using efficient implementations of the above, experiments are conducted over a wide range of benchmarks. The results demonstrate that: (i) the variable order generated by our approach significantly improves the performance of SAT solvers; (ii) time to derive this order is a fraction of the overall solving time. As a result, our approach delivers faster performance as compared to contemporary approaches.

We present an improvement to the preprocessing algorithm that was suggested by Bacchus and Winter in SAT 2003 [1]. Given the power of modern SAT solvers, is currently one of the only cost-effective preprocessors, at least when combined with some modern SAT solvers and on certain classes of problems. Our algorithm, although it produces less information than , is much more efficient. Experiments on a large set of industrial Benchmark sets from previous SAT competitions show that is always faster than (sometimes an order of magnitude faster on some of the bigger CNF formulas), and achieves faster total run times, including the SAT solver’s time. The experiments also show that is cost-effective when combined with three state-of-the-art SAT solvers.

Currently best known upper bounds for many NP-hard problems are obtained by using divide-and-conquer (splitting) algorithms. Roughly speaking, there are two ways of splitting algorithm improvement: a more involved case analysis and an introduction of a new simplification rule. It is clear that case analysis can be executed by computer, so it was considered as a machine task. Recently, several programs for automated case analysis were implemented. However, designing a new simplification rule is usually considered as a human task. In this paper we show that designing simplification rules can also be automated. We present several new (previously unknown) automatically generated simplification rules for the SAT and MAXSAT problems. The new approach allows not only to generate simplification rules, but also to find good splittings. To illustrate our technique we present a new algorithm for (,3)-MAXSAT that uses both splittings and simplification rules based on our approach and has worst-case running time (1.2721), where is the number of variables and is the length of an input formula. This bound improves the previously known bound (1.3248) of Bansal and Raman.

This paper describes and compares features and techniques modern SAT solvers utilize to maximize performance. Here we focus on: Implication Queue Sorting (IQS) combined with Early Conflict Detection Based BCP (ECDB); and a modified decision heuristic based on the combination of Variable State Independent Decaying Sum (VSIDS), Berkmin, and Siege’s Variable Move to Front (VMTF). These features were implemented and compared within the framework of the MIRA SAT solver. The efficient implementation and analysis of these features are presented and the speedup and robustness each feature provides is demonstrated. Finally, with everything enabled (ECDB with IQS and advanced decision heuristics), MIRA was able to consistently outperform zChaff and even Forklift on the benchmarks provided, solving 37 out of 111 industrial benchmarks compared to zChaff’s 21 and Forklift’s 28.

This paper describes a novel Field Programmable Gate Array (FPGA) logic synthesis technique which determines if a logic function can be implemented in a given programmable circuit and describes how this problem can be formalized and solved using Quantified Boolean Satisfiability. This technique is general enough to be applied to any type of logic function and programmable circuit; thus, it has many applications to FPGAs. The applications demonstrated in this paper include FPGA technology mapping and resynthesis where their results show significant FPGA performance improvements.

The utilization of cutting planes is a key technique in Integer Linear Programming (ILP). However, cutting planes have seldom been applied in Pseudo-Boolean Optimization (PBO) algorithms derived from the Davis-Logemann-Loveland (DLL) procedure for Propositional Satisfiability (SAT). This paper proposes the utilization of cutting planes in a DLL-style PBO algorithm, which incorporates the most effective techniques for PBO. We propose the utilization of cutting planes both during preprocessing and during the search process. Moreover, we also establish conditions that enable clause learning and non-chronological backtracking in the presence of conflicts involving constraints generated by cutting plane techniques. The experimental results, obtained on a large number of classes of instances, indicate that the integration of cutting planes with backtrack search is an extremely effective technique for PBO.

We propose a new benchmark set consisting of problems generated during the construction of classification theorems for quasigroups. It extends and generalises the domain of quasigroup existence problems, to which SAT solvers have been applied successfully in the past, to a rich class of benchmarks of varying difficulty.

We tackle the problem of finding a smallest-cardinality MUS (SMUS) of a given formula. The SMUS provides a succinct explanation of infeasibility and is valuable for applications that rely on such explanations. We present a branch-and-bound algorithm that utilizes iterative MAXSAT solutions to generate lower and upper bounds on the size of the SMUS, and branch on specific subformulas to find it. We report experimental results on formulas from DIMACS and DaimlerChrysler product configuration suites.