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Generic Complexity of Finitely Presented Monoids and Semigroups

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Abstract

We study the generic properties of finitely presented monoids and semigroups, and the generic-case complexity of decision problems for them. We show that for a finite alphabet A of size at least 2 and positive integers k and m, the generic A-generated k-relation monoid and semigroup (defined using any of several stratifications) satisfies the small overlap condition C(m). It follows that the generic finitely presented monoid has a number of interesting semigroup-theoretic properties and, by a recent result of the author, admits a linear time solution to its word problem and a regular language of unique normal forms for its elements. Moreover, the uniform word problem for finitely presented monoids is generically solvable in polynomial time.

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  1. School of Mathematics, University of Manchester, Manchester, M13 9PL, England, UK

    Mark Kambites

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  1. Mark Kambites
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Correspondence to Mark Kambites.

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Kambites, M. Generic Complexity of Finitely Presented Monoids and Semigroups. comput. complex. 20, 21–50 (2011). https://doi.org/10.1007/s00037-011-0005-5

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  • DOI: https://doi.org/10.1007/s00037-011-0005-5

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