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.

SAT Competition 2002 held in March--May 2002 in conjunction with SAT 2002 (the Fifth International Symposium on the Theory and Applications of Satisfiability Testing). About 30 solvers and 2300 benchmarks took part in the competition, which required more than 2 CPU years to complete the evaluation. In this report

Much recent work has gone into adapting techniques that were originally developed for SAT solving to QBF solving. In particular, QBF solvers are often based on SAT solvers. Most competitive QBF solvers are search-based. In this work we explore an alternative approach to QBF solving, based on symbolic quantifier elimination. We extend some recent symbolic approaches for SAT solving to symbolic QBF solving, using various decision-diagram formalisms such as OBDDs and ZDDs. In both approaches, QBF formulas are solved by eliminating all their quantifiers. Our first solver, QMRES, maintains a set of clauses represented by a ZDD and eliminates quantifiers via multi-resolution. Our second solver, QBDD, maintains a set of OBDDs, and eliminate quantifier by applying them to the underlying OBDDs. We compare our symbolic solvers to several competitive search-based solvers. We show that QBDD is not competitive, but QMRES compares favorably with search-based solvers on various benchmarks consisting of non-random formulas.

diagnosis rules that are more useful for fault diagnosis. In diagnosis the objective is to determine the modes of components that agree with the current observations. A partial diagnosis resolves a conflict of some specified observations. The first online step in Mini-ME is triggering rules. If the observation in a partial diagnosis rule corresponds to the current observation, then the component modes the rule implies are the relevant partial diagnoses. The advantage of Mini-ME over other model-based fault diagnosis systems is that the NP-complete satisfiability problem is removed from online computation. Instead of requiring possibly an exponential satisfiability search, Mini-ME generates partial diagnoses in time that is linear in the number of rules associated with a set of observations. First introduced in GDE [1], the final step in MiniME is to generate the most likely kernel diagnosis from the partial diagnoses. A kernel diagnosis is a minimal set of component modes that resolv

Abstract. Recent work has shown how to use OBDDs for satisfiability solving. The idea of this approach, which we call symbolic quantifier elimination, is to view an instance of propositional satisfiability as an existentially quantified propositional formula. Satisfiability solving then amounts to quantifier elimination; once all quantifiers have been eliminated we are left with either 1 or 0. Our goal in this work is to study the effectiveness of symbolic quantifier elimination as an approach to satisfiability solving. To that end, we conduct a direct comparison with the DPLL-based ZChaff, as well as evaluate a variety of optimization techniques for the symbolic approach. In comparing the symbolic approach to ZChaff, we evaluate scalability across a variety of classes of formulas. We find that no approach dominates across all classes. While ZChaff dominates for many classes of formulas, the symbolic approach is superior for other classes of formulas. Once we have demonstrated the viability of the symbolic approach, we focus on optimization techniques for this approach. We study techniques from constraint satisfaction for finding a good plan for performing the symbolic operations of conjunction and of existential quantification. We also study various variable-ordering heuristics, finding that while no heuristic seems to dominate across all classes of formulas, the maximum-cardinality search heuristic seems to offer the best overall performance. 1

Leading algorithms for Boolean satisfiability (SAT) are based on either a depth-first tree traversal of the search space (the DLL procedure [6]) or resolution (the DP procedure [7]). In this work we introduce a variant of BreadthFirst Search (BFS) based on the ability of Zero-Suppressed Binary Decision Diagrams (ZDDs) to compactly represent sparse or structured collections of subsets.

Abstract. Propositional proof complexity is the study of the sizes of propositional proofs, and more generally, the resources necessary to certify propositional tautologies. Questions about proof sizes have connections with computational complexity, theories of arithmetic, and satisfiability algorithms. This is article includes a broad survey of the field, and a technical exposition of some recently developed techniques for proving lower bounds on proof sizes. Contents

We present an extensive experimental study of consequence-finding algorithms based on kernel resolution, using both a trie-based and a novel ZBDD-based implementation, which uses Zero-Suppressed Binary Decision Diagrams to concisely store and process very large clause sets. Our study considers both the full prime implicate task and applications of consequence-finding for restricted target languages in abduction, model-based and fault-tree diagnosis, and polynomially-bounded knowledge compilation. We show that the ZBDD implementation can push consequence-finding to a new limit, solving problems which generate over 10^70 clauses.

SatEx is a web site devoted to SAT experimentation. It is not only a front end to a database gathering an exhaustive number of executions, but it also allows dynamic results synthesis as well as detailed explorations of experimentation results. Being dynamically generated and constantly updated and improved, this site can be considered as an almost always up-to-date SAT experimentation paper. To the current time, SatEx presents the results of more than 450 CPU days on a recent machine. In a few months, this site has been well received by the SAT community and has reached more than 20000 hits. SatEx site is available at http://www.lri.fr/simon/satex/satex.php3. 1

Patterns of contrast are a very important way of comparing multidimensional datasets. Such patterns are able to capture regions of high difference between two classes of data, and are useful for human experts and the construction of classifiers. However, mining such patterns is particularly challenging when the number of dimensions is large. This paper describes a new technique for mining several varieties of contrast pattern, based on the use of Zero-Suppressed Binary Decision Diagrams (ZBDDs), a powerful data structure for manipulating sparse data. We study the mining of both simple contrast patterns, such as emerging patterns, and more novel and complex contrasts, which we call disjunctive emerging patterns. A performance study demonstrates our ZBDD technique is highly scalable, substantially improves on state of the art mining for emerging patterns and can be effective for discovering complex contrasts from datasets with thousands of attributes.