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Abstract: In [7] the notions of recognition by semigroups and by programs over semigroups were extended to groupoids. This led to a new characterization of the context-free languages and the class SAC 1 . In this paper, we investigate the classes of languages obtained when the groupoids are restricted to be quasigroups (i.e. the multiplication table forms a latin square). We prove that languages recognized by quasigroups are regular and that programs over quasigroups characterize NC 1 . We... (Update)
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BibTeX entry: (Update)
H. Caussinus and F. Lemieux, "The Complexity of Computing over Quasigroups", In the Proceedings of the 14th annual FST&TCS Conference, pp.36-47, 1994. http://citeseer.ist.psu.edu/caussinus94complexity.html More
@inproceedings{ caussinus94complexity,
author = "Herve Caussinus and Francois Lemieux",
title = "The Complexity of Computing over Quasigroups",
booktitle = "Foundations of Software Technology and Theoretical Computer Science",
pages = "36-47",
year = "1994",
url = "citeseer.ist.psu.edu/caussinus94complexity.html" }
Citations (may not include all citations):168 A Taxonomy of Problems with Fast Parallel Algorithms (context) - Cook - 1985
121 and Machines (context) - Eilenberg, Languages - 1974
114 Bounded-Width Polynomial-Size Branching Programs Recognize E.. (context) - Barrington - 1989
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27 Extensions to Barrington's M-program model - B'edard, Lemieux et al. - 1993
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14 Contributions to the Theory of Loops (context) - Bruck - 1946
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6 A Property of Finite Simple Non-abelian Groups (context) - Maurer, Rhodes - 1965
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