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

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...

Full description

Saved in:
Bibliographic Details
Published inTheoretical computer science Vol. 653; pp. 87 - 96
Main Authors Bourne, Tom, Ruškuc, Nik
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.11.2016
Subjects
Alphabets
Combinatorial analysis
Group theory
Languages
Mathematical analysis
Rees matrix semigroup
Regular language
Star-height
Subword
Star-height
Subword
Regular language
Rees matrix semigroup
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2016.09.024