Biautomatic Semigroups

摘要

We consider biautomatic semigroups. There are two different definitions of a biautomatic structure for a group in the literature; whilst these definitions are not equivalent, the idea of a biautomatic group is well defined, in that a group possesses one type of biautomatic structure if and only if it possesses the other. However the two definitions give rise to different notions of biautomaticity for semigroups and we study these ideas in this paper. In particular, we settle the question as to whether automaticity and biautomaticity are equivalent for semigroups by giving examples of semigroups which are automatic but not biautomatic.