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21
SATO: An efficient propositional prover
 in International Conference on Automated Deduction
, 1997
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A DavisPutnam Based Enumeration Algorithm for Linear PseudoBoolean Optimization
, 1995
"... The DavisPutnam 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 DPprocedure for solving the satisfiability problem of a set of linear pseudoBoolean (or 01) ..."
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Cited by 127 (2 self)
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The DavisPutnam 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 DPprocedure for solving the satisfiability problem of a set of linear pseudoBoolean (or 01) inequalities. We extend the method to solve linear 01 optimization problems, i.e. optimize a linear pseudoBoolean objective function w.r.t. a set of linear pseudoBoolean inequalities. The algorithm compares well with traditional linear programming based methods on a variety of standard 01 integer programming benchmarks.
PSATO: a Distributed Propositional Prover and Its Application to Quasigroup Problems
 Journal of Symbolic Computation
, 1996
"... This paper shows a way of using such resources to solve hard problems. ..."
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Cited by 86 (4 self)
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This paper shows a way of using such resources to solve hard problems.
Implementing the DavisPutnam Method
 Journal of Automated Reasoning
, 2000
"... The method proposed by Davis, Putnam, Logemann, and Loveland for propositional reasoning, often referred to as the DavisPutnam method, is one of the major practical methods for the satisfiability (SAT) problem of propositional logic. We show how to implement the DavisPutnam method efficiently usin ..."
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Cited by 59 (3 self)
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The method proposed by Davis, Putnam, Logemann, and Loveland for propositional reasoning, often referred to as the DavisPutnam method, is one of the major practical methods for the satisfiability (SAT) problem of propositional logic. We show how to implement the DavisPutnam 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 DavisPutnam 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.
Ordered Binary Decision Diagrams and the DavisPutnam Procedure
 IN PROC. OF THE 1ST INTERNATIONAL CONFERENCE ON CONSTRAINTS IN COMPUTATIONAL LOGICS
, 1994
"... We compare two prominent decision procedures for propositional logic: Ordered Binary Decision Diagrams (obdds) and the DavisPutnam procedure. Experimental results indicate that the DavisPutnam procedure outperforms obdds in hard constraintsatisfaction problems, while obdds are clearly superior for ..."
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Cited by 49 (1 self)
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We compare two prominent decision procedures for propositional logic: Ordered Binary Decision Diagrams (obdds) and the DavisPutnam procedure. Experimental results indicate that the DavisPutnam procedure outperforms obdds in hard constraintsatisfaction 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 constraintoriented and searchoriented procedures.
Equivalence in answer set programming
 In Proc. LOPSTR 2001, LNCS 2372
, 2001
"... Abstract. We study the notion of strong equivalence between two Answer Set programs and we show how some particular cases of testing strong equivalence between programs can be reduced to verify if a formula is a theorem in intuitionistic or classical logic. We present some program transformations ..."
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Cited by 25 (5 self)
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Abstract. We study the notion of strong equivalence between two Answer Set programs and we show how some particular cases of testing strong equivalence between programs can be reduced to verify if a formula is a theorem in intuitionistic or classical logic. We present some program transformations for disjunctive programs, which can be used to simplify the structure of programs and reduce their size. These transformations are shown to be of interest for both computational and theoretical reasons. Then we propose how to generalize such transformations to deal with free programs (which allow the use of default negation in the head of clauses). We also present a linear time transformation that can reduce an augmented logic program (which allows nested expressions in both the head and body of clauses) to a program consisting only of standard disjunctive clauses and constraints. 1
Solving Open Quasigroup Problems by Propositional Reasoning
 In Proceedings of the International Computer Symp
, 1994
"... . 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 propositi ..."
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Cited by 16 (1 self)
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. 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 NPcomplete problem, it is relatively easy to transform any NPcomplete 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: Theorem Proving by Model Generation
 in Proc. National Conference of American Association on Artificial Intelligence (AAAI94
, 1994
"... 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 propositiona ..."
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Cited by 15 (1 self)
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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...
PMSat: a parallel version of minisat
 Journal on Satisfiability, Boolean Modeling and Computation
"... Parallel computing has become an affordable reality forcing a shift in the programming paradigm from sequential to concurrent applications, specially those who demand much computational power or with large search spaces like SATsolvers. In this context we present the research, planning and implemen ..."
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Cited by 11 (0 self)
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Parallel computing has become an affordable reality forcing a shift in the programming paradigm from sequential to concurrent applications, specially those who demand much computational power or with large search spaces like SATsolvers. In this context we present the research, planning and implementation of PMSat: a parallel version of MiniSAT with MPI (Message Passing Interface) technology, to be executed in clusters or grids of computers. The main features of the program are described: search modes, search space pruning and share of learnt clauses. An analysis of its performance and load balance is also presented. Keywords: parallel computing, SATsolver, satisfiability, message passing interface
Introduction to the OBDD Algorithm for the ATP Community
, 1992
"... We describe in terms familiar to the automated reasoning community the graphbased 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 proposi ..."
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We describe in terms familiar to the automated reasoning community the graphbased 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 IFthenelse 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, exclusiveor, etc) by exploiting the fact that the tests are ordered. The second is that every distinct cano...