We compare SAT-checkers and decision diagrams on the evaluation of Boolean formulas produced in the formal verification of both correct and buggy versions of superscalar and VLIW microprocessors. We identify one SAT-checker that significantly outperforms the rest. We evaluate ways to enhance its performance by variations in the generation of the Boolean correctness formulas. We reassess optimizations previously used to speed up the formal verification and probe future challenges.

Local search algorithms are among the standard methods for solving hard combinatorial problems from various areas of Artificial Intelligence and Operations Research. For SAT, some of the most successful and powerful algorithms are based on stochastic local search and in the past 10 years a large number of such algorithms have been proposed and investigated. In this article, we focus on two particularly well-known families of local search algorithms for SAT, the GSAT and WalkSAT architectures. We present a detailed comparative analysis of these algorithms' performance using a benchmark set which contains instances from randomised distributions as well as SAT-encoded problems from various domains. We also investigate the robustness of the observed performance characteristics as algorithm-dependent and problem-dependent parameters are changed. Our empirical analysis gives a very detailed picture of the algorithms' performance for various domains of SAT problems; it also reveals a fundamental weakness in some of the best-performing algorithms and shows how this can be overcome.

The local search algorithm WSat is one of the most successful algorithms for solving the satisfiability (SAT) problem. It is notably e#ective at solving hard Random 3-SAT instances near the so-called `satisfiability threshold', but still shows a peak in search cost near the threshold and large variations in cost over di#erent instances. We make a number of significant contributions to the analysis of WSat on high-cost random instances, using the recently-introduced concept of the backbone of a SAT instance. The backbone is the set of literals which are entailed by an instance. We find that the number of solutions predicts the cost well for small-backbone instances but is much less relevant for the large-backbone instances which appear near the threshold and dominate in the overconstrained region. We show a very strong correlation between search cost and the Hamming distance to the nearest solution early in WSat's search. This pattern leads us to introduce a measure of the ba...

It is well known that the ratio of the number of clauses to the number of variables in a random k-SAT instance is highly correlated with the instance's empirical hardness. We consider the problem of identifying such features of random SAT instances automatically with machine learning. We describe and analyze models for three SAT solvers---kcnfs, oksolver and satz---and for two different distributions of instances: uniform random 3-SAT with varying ratio of clauses-to-variables, and uniform random 3-SAT with fixed ratio of clauses-tovariables.

Abstract. Constraint satisfaction problems can be SAT-encoded in more than one way, and the choice of encoding can be as important as the choice of search algorithm. Theoretical results are few but experimental comparisons have been made between encodings, using both local and backtrack search algorithms. This paper compares local search performance on seven encodings of graph colouring benchmarks. Two of the encodings are new and one of them gives generally better results than known encodings. We also find better results than expected for two variants of the log encoding, and surprisingly poor results for the support encoding. 1

Programmers have long used assertions to characterize properties of code. An assertion violation signals a corruption in the program state. At such a state, it is standard to terminate the program, debug it if possible, and re-execute it. We propose a new view: instead of terminating the program, use the violated assertion as a basis of repairing the state of the program and let it continue. We present a novel algorithm to repair complex data structures. Given a structure that violates an assertion that represents its integrity constraints, our algorithm performs a systematic search based on symbolic execution to repair the structure, i.e., mutate it such that the resulting structure satisfies the given constraints. Heuristics to prune search and minimize mutations enable efficient and effective repair. Experiments using libraries and applications, such as a naming architecture and a database engine, show that our prototype efficiently repairs complex structures while enabling systems to recover from potentially crippling errors.

Abstract. Recent research has shown that it is often preferable to encode realworld problems as propositional satisfiability (SAT) problems, and then solve using general purpose solvers. In this way the efficiencies of SAT technology can be exploited, and the development of specialised solution techniques can be avoided. However, in the interval algebra (IA) domain of temporal reasoning, the state-of-the-art still involves the use of specialised techniques that exploit the particular structure of interval relations. In this paper we investigate the feasibility of representing and solving IA problems as SAT problems. We firstly introduce two methods of representing IA as a constraint satisfaction problem (CSP), and then use three SAT-encoding schemes to produce six different IA to SAT representations. In an empirical study, we examine the performance of existing SAT local and complete search solvers on these SAT representations, and perform a comparison with solvers that operate on native IA representations. Our results show that the best performance over a range of algorithms is produced using a support SAT encoding of a point algebra-based CSP. The results also show that a state-of-the-art complete SAT solver (zChaff) can solve these instances significantly faster than existing IA solvers working on equivalent native IA representations. 1

Constraint satisfaction problems can be SAT-encoded in more than one way, and the choice of encoding can be as important as the choice of search algorithm. Theoretical results are few but experimental comparisons have been made between encodings, using both local and backtrack search algorithms. This paper compares local search performance on seven encodings of graph colouring benchmarks. Two of the encodings are new, and one of these gives generally better results than known encodings. We also find better results than expected for the log encoding and one of its variants.

Stochastic Local Search (SLS) algorithms are amongst the most effective approaches for solving hard and large propositional satisfiability (SAT) problems. Prominent and successful SLS algorithms for SAT, including many members of the WalkSAT and GSAT families of algorithms, tend to show highly regular behaviour when applied to hard SAT instances: The run-time distributions (RTDs) of these algorithms are closely approximated by exponential distributions.

Multiple sequence alignment is a central problem in Bioinformatics and a challenging one for optimisation algorithms. An established integer programming approach is to apply branch-and-cut to a graph-theoretical model. The models are exponentially large but are represented intensionally, and violated constraints can be located in polynomial time. This report describes a new integer program formulation that generates polynomial-sized models small enough to be passed to generic solvers. It is a hybrid formulation relating the sparse alignment graph with a compact encoding of the alignment matrix via channelling constraints. Alignments obtained with a pseudo-Boolean local search algorithm are competitive with those of state-of-the-art algorithms. Execution times are much longer, but in future work we aim to develop a more efficient specialised algorithm. 1