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The TPTP Problem Library
, 1999
"... This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for buildin ..."
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Cited by 100 (6 self)
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This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for building the library; ffl a discussion of the inadequacies of previous problem collections, and how these have been resolved in the TPTP; ffl a description of the library structure, including overview information; ffl descriptions of supplementary utility programs; ffl guidelines for obtaining and using the library; Contents 1 Introduction 2 1.1 Previous Problem Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 What is Required? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Inside the TPTP 6 2.1 The TPTP Domain Structure . . . . . . . . . . . . . . . . . . . . . ...
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 68 (4 self)
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This paper shows a way of using such resources to solve hard problems.
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.
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 ...
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
HPMDs of type 2 n 3 1 with Block Size Four and Related HCOLSs
"... A holey perfect Mendelsohn design of type h n 1 1 h n 2 2 \Delta \Delta \Delta h n k k (HPMD(h n 1 1 h n 2 2 \Delta \Delta \Delta h n k k ) with block size four is equivalent to a frame idempotent quasigroup satisfying Stein's third law with the same type, where a frame quasigroup ..."
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A holey perfect Mendelsohn design of type h n 1 1 h n 2 2 \Delta \Delta \Delta h n k k (HPMD(h n 1 1 h n 2 2 \Delta \Delta \Delta h n k k ) with block size four is equivalent to a frame idempotent quasigroup satisfying Stein's third law with the same type, where a frame quasigroup of type h n1 1 h n2 2 \Delta \Delta \Delta h n k k means a quasigroup of order n with n i missing subquasigroups (holes) of order h i ; 1 i k, which are disjoint and spanning, that is P 1ik n i h i = n. In this paper, we investigate the existence of HPMD(2 n 3 1 ) and show that an HPMD(2 n 3 1 ) exists if and only if n 4. As an application, we readily obtain HSOLS(2 n 3 1 ) and establish the existence of (2,3,1) [or (3,1,2)]HCOLS(2 n 3 1 ) for all n 4. 1 Introduction A quasigroup is an ordered pair (Q; \Delta), where Q is a set and (\Delta) is a binary operation on Q such that the equations a \Delta x = b and y \Delta a = b (1) are uniquely solvable for e...
A DavisPutnam Program and its Application to Finite FirstOrder Model Search: Quasigroup Existence Problems
, 1994
"... This document describes the implementation and use of a DavisPutnam procedure for the propositional satisfiability problem. It also describes code that takes statements in firstorder logic with equality and a domain size n searches for models of size n. The firstorder modelsearching code transfor ..."
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This document describes the implementation and use of a DavisPutnam procedure for the propositional satisfiability problem. It also describes code that takes statements in firstorder logic with equality and a domain size n searches for models of size n. The firstorder modelsearching code transforms the statements into set of propositional clauses such that the firstorder statements have a model of size n if and only if the propositional clauses are satisfiable. The propositional set is then given to the DavisPutnam code; any propositional models that are found can be translated to models of the firstorder statements. The firstorder modelsearching program accepts statements only in a flattened relational clause form without function symbols. Additional code was written to take input statements in the language of Otter 3.0 [5] and produce the flattened relational form. The program was successfully applied to several open questions on the existence of orthogonal quasigroups. 1 The ...