A New Set of Algebraic Benchmark Problems for SAT Solvers

We propose a new benchmark set consisting of problems generated during the construction of classification theorems for quasigroups. It extends and generalises the domain of quasigroup existence problems, to which SAT solvers have been applied successfully in the past, to a rich class of benchmarks of varying difficulty.

[1]  Andrei Voronkov,et al.  Automated Deduction—CADE-18 , 2002, Lecture Notes in Computer Science.

[2]  Christoph Weidenbach,et al.  Computing Small Clause Normal Forms , 2001, Handbook of Automated Reasoning.

[3]  Alexander Russell,et al.  Approximating Latin Square Extensions , 1996, COCOON.

[4]  Simon Colton,et al.  Automatic Generation of Classification Theorems for Finite Algebras , 2004, IJCAR.

[5]  Masayuki Fujita,et al.  Automatic Generation of Some Results in Finite Algebra , 1993, IJCAI.

[6]  Alan Robinson,et al.  Handbook of automated reasoning , 2001 .

[7]  Alexander Russell,et al.  Approximating Latin Square Extensions , 1996, Algorithmica.

[8]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[9]  Robert Veroff,et al.  Automated Reasoning and Its Applications: Essays in Honor of Larry Wos , 1997 .

[10]  Christoph Weidenbach,et al.  S PASS Version 2.0 , 2002, CADE.

[11]  Sergey Berezin,et al.  CVC Lite: A New Implementation of the Cooperating Validity Checker Category B , 2004, CAV.

[12]  Robert A. Beezer.  Discrete Mathematics Using Latin Squares, by Charles F. Laywine, Gary L. Mullen , 2002 .

[13]  Cesare Tinelli,et al.  DPLL( T): Fast Decision Procedures , 2004, CAV.

[14]  Hantao Zhang.  Solving Open Quasigroup Problems by Propositional Reasoning , 1994 .

[15]  Volker Sorge,et al.  Applying SAT Solving in Classification of Finite Algebras , 2005, Journal of Automated Reasoning.

[16]  Larry Wos,et al.  What Is Automated Reasoning? , 1987, J. Autom. Reason..

[17]  G. Mullen,et al.  Discrete Mathematics Using Latin Squares , 1998, The Mathematical Gazette.

[18]  Maria Paola Bonacina,et al.  PSATO: a Distributed Propositional Prover and its Application to Quasigroup Problems , 1996, J. Symb. Comput..

[19]  W. McCune.  A Davis-Putnam program and its application to finite-order model search: Quasigroup existence problems , 1994 .