Two variants of the Froiduire-Pin Algorithm for finite semigroups
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In this paper, we present two algorithms based on the Froidure-Pin Algorithm for computing the structure of a finite semigroup from a generating set. As was the case with the original algorithm of Froidure and Pin, the algorithms presented here produce the left and right Cayley graphs, a confluent terminating rewriting system, and a reduced word of the rewriting system for every element of the semigroup. If U is any semigroup, and A is a subset of U, then we denote by 〈 A〉 the least subsemigroup of U containing A. If B is any other subset of U, then, roughly speaking, the first algorithm we present describes how to use any information about 〈 A〉, that has been found using the Froidure-Pin Algorithm, to compute the semigroup 〈 A∪ B〉. More precisely, we describe the data structure for a finite semigroup S given by Froidure and Pin, and how to obtain such a data structure for 〈 A∪ B〉 from that for 〈 A〉. The second algorithm is a lock-free concurrent version of the Froidure-Pin Algorithm.
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