Studying quasigroup identities by rewriting techniques: Problems and first results
Finite quasigroups in the form of Latin squares have been extensively studied in design theory. Some quasigroups satisfy constraints in the form of equations, called quasigroup identities. In this note, we propose some questions concerning quasigroup identities that can sometimes be answered by the rewriting techniques.
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- 1.Bennett, F.: The spectra of a variety of quasigroups and related combinatorial designs. Discrete Math. 34 (1987): 43–64.Google Scholar
- 2.Bennett, F., Zhu, L.: Conjugate-orthogonal Latin squares and related structures, J. Dinitz & D. Stinson (eds), Contemporary Design Theory: A Collection of Surveys. John Wiley & Sons, 1992.Google Scholar
- 3.Evans, T.: Algebraic structures associated with Latin squares and orthogonal arrays. Proc. of Conf. on Algebraic Aspects of Combinatorics. Congr. Numer. 13 (1975): 31–52.Google Scholar
- 4.Fujita, M., Slaney, J., Bennett, F.: Automatic generation of some results in finite algebra, Proc. International Joint Conference on Artificial Intelligence, 1993.Google Scholar
- 5.McCune, W.: A Davis-Putnam program and its application to finite first-order model search: quasigroup existence problems. Preprint, Division of MCS, Argonne National Laboratory, 1994.Google Scholar
- 6.Slaney, J., Fujita, M., Stickel, M.: Automated reasoning and exhaustive search: Quasigroup existence problems. To appear in Computers and Mathematics with Applications, 1994.Google Scholar
- 7.Zhang, H., Bonacina, M. P.: Cumulating search in a distributed computing environment: a case study in parallel satisfiability. Proc. of the First International Symposium on Parallel Symbolic Computation. Sept. 26–28, 1994, Linz, Austria.Google Scholar
- 8.Zhang, H., Hsiang, J.: Solving open quasigroup problems by propositional reasoning. Proc. of International Computer Symposium, Taiwan, December 1994.Google Scholar
- 9.Zhang, H., Stickel, M.: Implementing the Davis-Putnam algorithm by tries. Technical Report, Dept. of Computer Science, The University of Iowa, 1994.Google Scholar
- 10.Zhang, J.: Search for idempotent models of quasigroup identities, Typescript, Institute of Software, Academia Sinica, Beijing, 1991.Google Scholar