Small overlap monoids: the word problem

Details Small overlap monoids: the word problem Small overlap monoids: the word problem

2007-12-03

arxiv.org/abs/0712.0250v1

Mathematics

Rings and Algebras

22 pages

Scientific paper

We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis of words which lends itself to the development of practical, efficient computational algorithms. In particular, we obtain a highly practical linear time solution to the word problem for monoids and semigroups with finite presentations satisfying the condition C(4), and a polynomial time solution to the uniform word problem for presentations satisfying the same condition.

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