Catálogo de publicaciones - libros

We consider the -satisfiability problem. It is known that the random -SAT model, in which the instance is a set of -clauses selected uniformly from the set of all -clauses over variables, has a phase transition at a certain clause density, below which most instances are satisfiable and above which most instances are unsatisfiable. The essential feature of the random -SAT is that positive and negative literals occur with equal probability in a random formula. How does the phase transition behavior change as the relative probability of positive and negative literals changes?

In this paper we focus on a distribution in which positive and negative literals occur with different probability. We present empirical evidence for the satisfiability phase transition for this distribution. We also prove an upper bound on the satisfiability threshold and a linear lower bound on the number of literals in satisfying partial assignments of skewed random -SAT formulas.

The original algorithm for the SAT problem, Variable Elimination Resolution (VER/DP) has exponential space complexity. To tackle that, the backtracking-based DPLL procedure [2] is used in SAT solvers. We present a combination of two techniques: we use NiVER, a special case of VER, to eliminate some variables in a preprocessing step, and then solve the simplified problem using a DPLL SAT solver. NiVER is a strictly formula size not increasing resolution based preprocessor. In the experiments, NiVER resulted in up to 74% decrease in (Number of variables), 58% decrease in (Number of clauses) and 46% decrease in (Literal count). In many real-life instances, we observed that most of the resolvents for several variables are tautologies. Such variables are removed by NiVER. Hence, despite its simplicity, NiVER does result in easier instances. In case NiVER removable variables are not present, due to very low overhead, the cost of NiVER is insignificant. Empirical results using the state-of-the-art SAT solvers show the usefulness of NiVER. Some instances cannot be solved without NiVER preprocessing. NiVER consistently performs well and hence, can be incorporated into all general purpose SAT solvers.

The sequential circuit state space diameter problem is an important problem in sequential verification. Bounded model checking is complete if the state space diameter of the system is known. By unrolling the transition relation, the sequential circuit state space diameter problem can be formulated as either a series of Boolean satisfiability (SAT) problems or an evaluation for satisfiability of a Quantified Boolean Formula (QBF). Thus far neither the SAT based technique that uses sophisticated SAT solvers, nor QBF evaluations for the various QBF formulations for this have fared well in practice. The poor performance of the QBF evaluations is blamed on the relative immaturity of QBF solvers, with hope that ongoing research in QBF solvers could lead to practical success here.

Most existing QBF algorithms, such as those based on the DPLL SAT algorithm, are search based. We show that using search based QBF algorithms to calculate the state space diameter of sequential circuits with existing problem formulations is no better than using SAT to solve this problem. This result holds independent of the representation of the QBF formula. This result is important as it highlights the need to explore non-search based or hybrid of search and non-search based QBF algorithms for the sequential circuit state space diameter problem.

In this paper we introduce UBCSAT, a new implementation and experimentation environment for Stochastic Local Search (SLS) algorithms for SAT and MAX-SAT. Based on a novel triggered procedure architecture, UBCSAT provides implementations of numerous well-known and widely used SLS algorithms for SAT and MAX-SAT, including GSAT, WalkSAT, and SAPS; these implementations generally match or exceed the efficiency of the respective original reference implementations. Through numerous reporting and statistical features, including the measurement of run-time distributions, UBCSAT facilitates the advanced empirical analysis of these algorithms. New algorithm variants, SLS algorithms, and reporting features can be added to UBCSAT in a straightforward and efficient way. UBCSAT is implemented in C and runs on numerous platforms and operating systems; it is publicly and freely available at .

For the third consecutive year, a SAT competition was organized as a joint event with the SAT conference. With 55 solvers from 25 author groups, the competition was a clear success. One of the noticeable facts from the 2004 competition is the superiority of incomplete solvers on satisfiable random k-SAT benchmarks. It can also be pointed out that the complete solvers awarded this year, namely Zchaff, and march-eq, participated in the SAT 2003 competition (or at least former versions of those solvers). This paper is not reporting exhaustive competition results, already available in details online, but rather focuses on some remarkable results derived from the competition dataset.

The SAT 2004 competition is ending a 3-year take-off period that attracted new SAT researchers and provided many new benchmarks and solvers to the community. The good participation rate of this year (despite the addition of the anti-blackbox rule) establishes the competition as an awaited yearly event. Some new directions for a new way of thinking about the competition are discussed at the end of the paper.

This paper discusses several techniques to make the look- ahead architecture for satisfiability solvers more competitive. Our contribution consists of reduction of the computational costs to perform look-ahead and a cheap integration of both equivalence reasoning and local learning. Most proposed techniques are illustrated with experimental results of their implementation in our solver march_eq.

The Boolean Satisfiability Problem (SAT) is a well known NP-Complete problem. While its complexity remains a source of many interesting questions for theoretical computer scientists, the problem has found many practical applications in recent years. The emergence of efficient SAT solvers which can handle large structured SAT instances has enabled the use of SAT solvers in diverse domains such as electronic design automation and artificial intelligence. These applications continue to motivate the development of faster and more robust SAT solvers. In this paper, we describe the popular SAT solver zchaff with a focus on recent developments.

This paper reports about the 2004 comparative evaluation of solvers for quantified Boolean formulas (QBFs), the second in a series of non-competitive events established with the aim of assessing the advancements in the field of QBF reasoning and related research. We evaluated sixteen solvers on a test set of about one thousand benchmarks selected from instances submitted to the evaluation and from those available at . In the paper we present the evaluation infrastructure, from the criteria used to select the benchmarks to the hardware set up, and we show different views about the results obtained, highlighting the strength of different solvers and the relative hardness of the benchmarks included in the test set.