r class of SAT instances. For instance, in our study of quasigroup problems, one rule seems better than the others: choose one literal in one of the shortest positive clauses (a positive clause is a clause where all the literals are positive). On the other hand, a proved effective splitting rule is to choose a variable x such that the value f 2 (x) f 2 (:x) is maximal, where f 2 (L) is one plus the number of occurrences of literal L in binary clauses [2, 5]. We tried to combine the above two rules into one as follows: Let 0 ! a 1 and n be the number of shortest non-Horn clauses in the current set. At first, we collect all the variable names appearing in the first da ne shortest positive clauses. Then we choose x in this pool

The Davis-Putnam enumeration method (DP) has recently become one of the fastest known methods for solving the clausal satisfiability problem of propositional calculus. We present a generalization of the DP-procedure for solving the satisfiability problem of a set of linear pseudo-Boolean (or 0-1) inequalities. We extend the method to solve linear 0-1 optimization problems, i.e. optimize a linear pseudo-Boolean objective function w.r.t. a set of linear pseudo-Boolean inequalities. The algorithm compares well with traditional linear programming based methods on a variety of standard 0-1 integer programming benchmarks. Keywords 0-1 Integer Programming; Propositional Calculus; Enumeration Contents 1 Introduction 1 2 Preliminaries 1 3 The Classical Davis-Putnam Procedure 3 4 Davis-Putnam for Linear Pseudo-Boolean Inequalities 5 5 Optimizing with Pseudo-Boolean Davis-Putnam 7 6 Implementation 8 7 Heuristics 10 8 Computational Results 10 9 Conclusion 12 1 Introduction The Davis-Putn...

This paper shows a way of using such resources to solve hard problems.

The method proposed by Davis, Putnam, Logemann, and Loveland for propositional reasoning, often referred to as the Davis-Putnam method, is one of the major practical methods for the satisfiability (SAT) problem of propositional logic. We show how to implement the Davis-Putnam method efficiently using the trie data structure for propositional clauses. A new technique of indexing only the first and last literals of clauses yields a unit propagation procedure whose complexity is sublinear to the number of occurrences of the variable in the input. We also show that the Davis-Putnam method can work better when unit subsumption is not used. We illustrate the performance of our programs on some quasigroup problems. The efficiency of our programs has enabled us to solve some open quasigroup problems.

We compare two prominent decision procedures for propositional logic: Ordered Binary Decision Diagrams (obdds) and the DavisPutnam procedure. Experimental results indicate that the Davis-Putnam procedure outperforms obdds in hard constraint-satisfaction problems, while obdds are clearly superior for Boolean functional equivalence problems from the circuit domain, and, in general, problems that require the schematization of a large number of solutions that share a common structure. The two methods illustrate the different and often complementary strengths of constraint-oriented and search-oriented procedures.

We study the problem of determining if two programs are strongly equivalent in ASP (Answer set programming). We show how to reduce some subcases of this problem to provability in intuitionistic /classical logic. We also present a linear reduction of free programs (general programs extended to possibly include negated atoms in their heads) into standard general programs.

. There are many open problems in the study of quasigroups. Recently, automated techniques have been employed to attack these open problems. In this paper, we show how a propositional satisfiability prover is used to solve many open problems in quasigroups. Our success relies on a powerful propositional prover called SATO and a useful technique called the cyclic group construction. We provide detailed solutions to open problems solved by SATO. 1 Introduction In the recent years, there has been considerable renewed interest in the propositional satisfiability problem (SAT). Because the SAT problem is the first known NP-complete problem, it is relatively easy to transform any NP-complete problem in mathematics, computer science and electrical engineering into the SAT problem. The SAT problem is known to be difficult to solve in theory. However, contrary to the common perception that transforming a problem into the SAT problem will not make the problem easier to solve, many problems can ...

ModGen (Model Generation) is a complete theorem prover for first order logic with finite Herbrand domains. ModGen takes first order formulas as input, and generates models of the input formulas. ModGen consists of two major modules: a module for transforming the input formulas into propositional clauses, and a module to find models of the propositional clauses. The first module can be used by other researchers so that the SAT problems can be easily represented, stored and communicated. An important issue in the design of ModGen is to ensure that transformed propositional clauses are satisfiable iff the original formulas are. The second module can be easily replaced by any advanced SAT problem solver. ModGen is easy to use and very efficient. Many problems which are hard for general resolution theorem provers are found easy for ModGen. Introduction Many theorem proving problems are difficult for today 's theorem provers not because these problems are really hard but be...

We describe in terms familiar to the automated reasoning community the graph-based algorithm for deciding propositional equivalence published by R.E. Bryant in 1986. Such algorithm, based on ordered binary decision diagrams or OBDDs, are currently the fastest known ways to decide whether two propositional expressions are equivalent and are generally hundreds or thousands of times faster on such problems than most automatic theorem proving systems. An OBDD is a normalized IF-then-else expression in which the tests down any branch are ascending in some previously chosen fixed order. Such IF expressions represent a canonical form for propositional expressions. Three coding tricks make it extremely efficient to manipulate canonical IF expressions. The first is that two canonicalized expressions can be rapidly combined to form the canonicalized form of their disjunction (conjunction, exclusive-or, etc) by exploiting the fact that the tests are ordered. The second is that every distinct cano...

: We present a parallel propositional satisfiability (SAT) prover called PSATO for networks of workstations. PSATO is based on the sequential SAT prover SATO, which is an efficient implementation of the Davis-Putnam algorithm. The master-slave model is used for communication. A simple and effective workload balancing method distributes the workload among workstations. A key property of our method is that the concurrent processes explore disjoint portions of the search space. In this way, we use parallelism without introducing redundant search. Our approach provides solutions to the problems of (i) cumulating intermediate results of separated runs of reasoning programs; (ii) designing high scalable parallel algorithms and (iii) supporting "fault-tolerant" distributed computing. Several open problems in the study of quasigroups have been solved using PSATO. Keywords: Distributed and parallel computing, propositional satisfiability, constraint satisfaction, fault-tolerant computing. 1 Int...