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arXiv · 0712.0250

Small overlap monoids: the word problem

Mark Kambites
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Abstract

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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Mark Kambites. 2007-12-03. Small overlap monoids: the word problem. https://arxiv.org/abs/0712.0250

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