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Computing Transformation Semigroups
 SUBMITTED TO JOURNAL OF SYMBOLIC COMPUTATION
"... This paper describes algorithms for computing the structure of finite transformation semigroups. The algorithms depend crucially on a new data structure for an Rclass in terms of a group and an action. They provide for local computations, concerning a single Rclass, without computing the whole sem ..."
Abstract

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This paper describes algorithms for computing the structure of finite transformation semigroups. The algorithms depend crucially on a new data structure for an Rclass in terms of a group and an action. They provide for local computations, concerning a single Rclass, without computing the whole semigroup, as well as for computing the global structure of the semigroup. The algorithms have been implemented in the share package MONOID within the GAP system for computational algebra.
ON FINITE PRESENTABILITY OF MONOIDS AND THEIR SCHÜTZENBERGER GROUPS
, 2000
"... The main result of this paper asserts that a monoid with finitely many left and right ideals is finitely presented if and only if all its Schützenberger groups are finitely presented. The most important part of the proof is a rewriting theorem, giving a presentation for a Schützenberger group, which ..."
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The main result of this paper asserts that a monoid with finitely many left and right ideals is finitely presented if and only if all its Schützenberger groups are finitely presented. The most important part of the proof is a rewriting theorem, giving a presentation for a Schützenberger group, which is similar to the ReidemeisterSchreier rewriting theorem for groups.
Author manuscript, published in "Foundations of Computational Mathematics, Rio de Janeiro: Brazil (1997)" Algorithms for computing finite semigroups
, 2007
"... The aim of this paper is to present algorithms to compute finite semigroups. The semigroup is given by a set of generators taken in a larger semigroup, called the “universe”. This universe can be for instance the semigroup of all functions, partial functions, or relations on the set {1,..., n}, or t ..."
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The aim of this paper is to present algorithms to compute finite semigroups. The semigroup is given by a set of generators taken in a larger semigroup, called the “universe”. This universe can be for instance the semigroup of all functions, partial functions, or relations on the set {1,..., n}, or the semigroup of n × n matrices with entries in a given finite semiring. The algorithm produces simultaneously a presentation of the semigroup by generators and relations, a confluent rewriting system for this presentation and the Cayley graph of the semigroup. The elements of the semigroup are identified with the reduced words of the rewriting system. We also give some efficient algorithms to compute the Green relations, the local subsemigroups and the syntactic quasiorder of a subset of the semigroup. 1