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SEM: A System for Enumerating Models
 Department of Philosophy University of WisconsinMadison Mathematics and Computer Science
, 1995
"... Model generation can be regarded as a special case of the Constraint Satisfaction Problem (CSP). It has many applications in AI, computer science and mathematics. In this paper, we describe SEM, a System for Enumerating finite Models of firstorder manysorted theories. To the best of our knowledge, ..."
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Cited by 70 (2 self)
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Model generation can be regarded as a special case of the Constraint Satisfaction Problem (CSP). It has many applications in AI, computer science and mathematics. In this paper, we describe SEM, a System for Enumerating finite Models of firstorder manysorted theories. To the best of our knowledge, SEM outperforms any other finite model generation system on many test problems. The high performance of SEM relies on the following two techniques: (a) an efficient implementation of constraint propagation which requires little dynamic allocation of storage; (b) a powerful heuristic which eliminates many isomorphic partial models during the search. We will present the basic algorithm of SEM along with these two techniques. Our experimental results show that general purpose finite model generators are indeed useful in many applications. 1
Automated Reasoning and Exhaustive Search: Quasigroup Existence Problems
, 1995
"... this paper we consider only exhaustive searching techniques rather than more radical ones such as genetic algorithms, simulated annealing or the like. Among search algorithms, we consider only backtracking methods to which the cardinality of the constraints is irrelevant. This narrowing of our focu ..."
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Cited by 56 (4 self)
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this paper we consider only exhaustive searching techniques rather than more radical ones such as genetic algorithms, simulated annealing or the like. Among search algorithms, we consider only backtracking methods to which the cardinality of the constraints is irrelevant. This narrowing of our focus is in no way intended to slight any of the alternative methods. Merely, our research is what it is and not another thing. It is extremely easy and natural to represent existence problems such as our QG1QG7 in terms of consistent labelling. To generate a quasigroup of order v is to fill in each of the v
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 53 (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.
Implementing the DavisPutnam Algorithm by Tries
 ARTIFICIAL INTELLIGENCE CENTER, SRI INTERNATIONAL, MENLO
, 1994
"... 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 by presenting seven implementations of the method. We prop ..."
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Cited by 37 (7 self)
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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 by presenting seven implementations of the method. We propose a new technique for implementing unit propagation whose complexity is sublinear to the number of occurrences of the variable in the input. We present the performance of our programs on some quasigroup problems. The efficiency of our programs allowed us to solve some open quasigroup problems.
Cumulating Search in a Distributed Computing Environment: A Case Study in Parallel Satisfiability
 Proc. of the First Int. Symp. on Parallel Symbolic Computation
, 1994
"... : 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 DavisPutnam algorithm. The masterslave model is used for communication. A simple and effective ..."
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Cited by 7 (2 self)
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: 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 DavisPutnam algorithm. The masterslave 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 "faulttolerant" distributed computing. Several open problems in the study of quasigroups have been solved using PSATO. Keywords: Distributed and parallel computing, propositional satisfiability, constraint satisfaction, faulttolerant computing. 1 Int...
Specifying Latin Square Problems in Propositional Logic
 In Automated Reasoning and Its Applications
, 1997
"... Introduction This chapter discusses how to specify various Latin squares so that their existence can be efficiently decided by computer programs. The computer programs considered here are socalled generalpurpose model generation programs (or simply model generators) that are used to solve constra ..."
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Cited by 3 (0 self)
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Introduction This chapter discusses how to specify various Latin squares so that their existence can be efficiently decided by computer programs. The computer programs considered here are socalled generalpurpose model generation programs (or simply model generators) that are used to solve constraint satisfaction problems in AI, to prove theorems in finite domains, or to produce counterexamples to false conjectures. For instance, any example of finite structures in Larry Wos's book [16] can be easily solved using these model generators. In the recent years, model generators have been used to solve the existence problem of Latin squares with specified properties. Numerous previously open cases of Latin squares were first solved by these model generators. These Latin square problems are attacked along the two lines: (a) develop efficient model generation programs; (b) provide efficient specifications of the same problem. This chapter will focus on the latter as we realize throu