On the star-height of subword counting languages and their relationship to Rees zero-matrix semigroups
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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.
Bourne , T & Ruškuc , N 2016 , ' On the star-height of subword counting languages and their relationship to Rees zero-matrix semigroups ' Theoretical Computer Science , vol 653 , pp. 87-96 . DOI: 10.1016/j.tcs.2016.09.024
Theoretical Computer Science
© 2016, Elsevier. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.sciencedirect.com / https://dx.doi.org/10.1016/j.tcs.2016.09.024
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