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arXiv · 1603.06236

On the star-height of factor counting languages and their relationship to Rees zero-matrix semigroups

Tom Bourne·Nik Ruskuc
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Abstract

Given a word $w$ over a finite alphabet, we consider, in three special cases, the generalised star-height of the languages in which $w$ occurs as a contiguous subword (factor) an exact number of times and of the languages in which $w$ occurs as a contiguous subword modulo a fixed number, and prove that in each case it is at most one. We use these combinatorial results to show that any language recognised by a Rees (zero-)matrix semigroup over an abelian group is of generalised star-height at most one.

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Tom Bourne, Nik Ruskuc. 2016-03-20. On the star-height of factor counting languages and their relationship to Rees zero-matrix semigroups. https://arxiv.org/abs/1603.06236

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