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- W2100069437 abstract "We study the way in which the abstract structure of a small overlap monoid is reflected in, and may be algorithmically deduced from, a small overlap presentation. We show that every C(2) monoid admits an essentially canonical C(2) presentation; by counting canonical presentations we obtain asymptotic estimates for the number of non-isomorphic monoids admitting a-generator, k-relation presentations of a given length. We demonstrate an algorithm to transform an arbitrary presentation for a C(m) monoid (m at least 2) into a canonical C(m) presentation, and a solution to the isomorphism problem for C(2) presentations. We also find a simple combinatorial condition on a C(4) presentation which is necessary and sufficient for the monoid presented to be left cancellative. We apply this to obtain algorithms to decide if a given C(4) monoid is left cancellative, right cancellative or cancellative, and to show that cancellativity properties are asymptotically visible in the sense of generic-case complexity." @default.
- W2100069437 created "2016-06-24" @default.
- W2100069437 creator A5041232556 @default.
- W2100069437 date "2009-10-26" @default.
- W2100069437 modified "2023-09-27" @default.
- W2100069437 title "Uniform decision problems and abstract properties of small overlap monoids" @default.
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