Space functions and complexity of the word problem in semigroups

Details Space functions and complexity of the word problem in semigroups Space functions and complexity of the word problem in semigroups

2011-11-06

arxiv.org/abs/1111.1458v1

Mathematics

Group Theory

29 pages, 10 figures

Scientific paper

We introduce the space function $s(n)$ of a finitely presented semigroup $S =.$ 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 $w=w_0\to...\to w_t= w'$; $s(n)$ bounds from above the tape space (or computer memory) sufficient to implement all such transitions $w\to...\to w'.$ 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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