Space functions and complexity of the word problem in semigroups
Abstract
We introduce the space function s(n) of a finitely presented semigroup S =<A R>. To define s(n) we consider pairs of words w,w' over A of length at most n equal in S and use relations from R for the transformations w=w0... wt= w'; s(n) bounds from above the tape space (or computer memory) sufficient to implement all such transitions w... w'. One of the results obtained is the following criterion: A finitely generated semigroup S has decidable word problem of polynomial space complexity if and only if S is a subsemigroup of a finitely presented semigroup H with polynomial space function.
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