Applying SAT solving in classification of finite algebras

Journal of Automated Reasoning

Volumn 35, Issue 1-3, 2005, Pages 201-235

  Meier, Andreas ^a   Sorge, Volker ^b  

^a GERMAN RESEARCH CENTER FOR ARTIFICIAL INTELLIGENCE DFKI   (Germany)

^b UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Application of SAT; Finite algebra; Mathematics

Indexed keywords

ALGORITHMS; CLASSIFICATION (OF INFORMATION); FINITE ELEMENT METHOD; PROBLEM SOLVING; THEOREM PROVING;

ALGEBRAIC STRUCTURES; BOOTSTRAPPING; FINITE ALGEBRA; SAT APPLICATIONS;

LINEAR ALGEBRA;

EID: 33749567951     PISSN: 01687433     EISSN: 15730670     Source Type: Journal    
DOI: 10.1007/s10817-005-9003-0     Document Type: Article

References (29)

1. Alur, R. and Peled, D. (eds.): Proc. of Computer Aided Verification, 16th International Conference, CAV 2004, Vol. 3114 of LNCS, Springer, 2004.
2. Audemard, G., Bertoli, P., Cimatti, A., Korniłowicz, A. and Sebastiani, R.: Integrating Boolean and mathematical solving: foundations, basic algorithms and requirements, in Proc. of CALCULEMUS-2002, Vol. 2385 of LNAI, 2002.
3. Barrett, C. and Berezin, S.: CVC Lite: A New Implementation of the Cooperating Validity Checker, in [1], 2004, pp. 515-518.
4. Colton, S.: The HR program for theorem generation, in [23], 2002.
5. Colton, S., Meier, A., Sorge, V. and McCasland, R.: Automatic generation of classification theorems for finite algebras, in Proc. of IJCAR 2004, Vol. 3097 of LNAI, 2004, pp. 400-414. Springer.
6. Fujita, M., Slaney, J. and Bennett, F.: Automatic generation of some results in finite algebra, in Proc. IJCAI-13, 1993, pp. 52-57.
7. Ganzinger, H., Hagen, G., Nieuwenhuis, R., Oliveras, A. and Tinelli, C.: DPLL(T): Fast Decision Procedures, in [1], 2004, pp. 175-188.
8. Gap: GAP Reference Manual, The GAP Group, School of Mathematical and Computational Sciences, University of St. Andrews, 2000.
9. Gomes, C. P., Selman, B., Crato, N. and Kautz, H.: Heavy-tailed phenomena in satisfiability and constraint satisfaction problems, J. Autom. Reason. 24 (2000), 67-100.
10. Kunen, K: Single axioms for groups, J. Autom. Reason. 9(3) (1992), 291-308.
11. McCune, W.: Single axioms for groups and Abelian groups with various operations, J. Autom. Reason. 10(1) (1993), 1-3.
12. McCune, W.: A Davis-Putnam program and its application to finite first order model search: quasigroup existence problems. Technical report ANL/MCS-TM-194, Argonne National Laboratory, Division of MSC, 1994.
13. McCune, W.: Mace4 Reference Manual and Guide, Argonne National Laboratory. ANL/MCS-TM-264, 2003.
14. Mckay, B. D., Meinart, A. and Myrvold, W.: Counting small Latin squares, in European Women in Mathematics Int. Workshop on Groups and Graphs, 2002, pp. 67-72.
15. McKay, B. D. and Wanless, I. M.: The number of Latin squares of order eleven. Submitted for publication. Available at http://cs.anu.edu.au/~bdm/ papers/1s11.pdf.
16. Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L. and Malik, S.: Chaff: engineering an efficient SAT solver, in Proc. of the Design Automation Conference, 2001, pp. 530-535.
17. Nonnengart, A. and Weidenbach, C.: Computing small clause normal forms, in Handbook of Automated Reasoning, Elsevier, 2001.
18. Pflugfelder, H. O.: Quasigroups and Loops: Introduction, Vol. 7 of Sigma Series in Pure Mathematics, Helderman Verlag, 1990.
19. Slaney, J.: FINDER, Notes and Guide, Center for Information Science Research Australian National University, 1995.
20. Slaney, J., Fujita, M. and Stickel, M. E.: Automated reasoning and exhaustive search: quasigroup existense problems, Comput. Math. Appl. 29 (1995), 115-132.
21. Sutcliffe, G.: The IJCAR-2004 Automated Theorem Proving Competition, AI Communications 18(1) (2005), 33-40.
22. Sutcliffe, G. and Suttner, C.: The TPTP problem library: CNF release v 1.2.1, J. Aut. Reason. 21(2) (1998), 177-203.
23. Voronkov, A. (ed.): Proc. of the 18th International Conference on Automated Deduction (CADE-18), Vol. 2392 of LNAI, Springer, 2002.
24. Weidenbach, C., Brahm, U., Hillenbrand, T., Keen, E., Theobald, C. and Topic, D.: SPASS Version 2.0. in [23], pp. 275-279.
25. Zhang, H.: SATO: an efficient prepositional prover, in Proc. of CADE-14, vol. 1249 of LNAI, 1997, pp. 272-275.
26. Zhang, H.: Specifying Latin squares in propositional logic, in Automated Reasoning and Its Applications, Essays in honor of Larry Wos, MIT Press, 1997.
27. Zhang, H., Bonacina, M. P. and Hsiang, J.: PSATO: a distributed propositional prover and its application to quasigroup problems, J. Symb. Comput. 21 (1996), 543-560.
28. Zhang, H. and Hsiang, J.: Solving open quasigroup problems by propositional reasoning, in Proc. of Int. Computer Symposium, Hsinchu, Taiwan, 1994.
29. Zhang, J. and Zhang, H.: SEM User's Guide, Department of Computer Science, University of Iowa, 2001.