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...

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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
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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.
AbstractList 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.
Author Bourne, Tom
Ruškuc, Nik
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Cites_doi 10.1016/0890-5401(92)90063-L
10.1016/0022-0000(83)90031-4
10.1307/mmj/1028998975
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Keywords Star-height
Subword
Regular language
Rees matrix semigroup
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References Eggan (br0010) 1963; 10
Pin, Straubing, Thérien (br0090) 1992; 101
Pin (br0070) 1986
Pin, Straubing, Therien (br0080) 1989; vol. 349
Eilenberg (br0030) 1976
Howie (br0060) 1995; vol. 12
Hashiguchi (br0040) 1983; 27
Henneman (br0050) 1971
Sakarovitch (br0100) 2009
Eilenberg (br0020) 1974
Eilenberg (10.1016/j.tcs.2016.09.024_br0020) 1974
Sakarovitch (10.1016/j.tcs.2016.09.024_br0100) 2009
Eggan (10.1016/j.tcs.2016.09.024_br0010) 1963; 10
Pin (10.1016/j.tcs.2016.09.024_br0080) 1989; vol. 349
Pin (10.1016/j.tcs.2016.09.024_br0090) 1992; 101
Hashiguchi (10.1016/j.tcs.2016.09.024_br0040) 1983; 27
Pin (10.1016/j.tcs.2016.09.024_br0070) 1986
Henneman (10.1016/j.tcs.2016.09.024_br0050) 1971
Eilenberg (10.1016/j.tcs.2016.09.024_br0030) 1976
Howie (10.1016/j.tcs.2016.09.024_br0060) 1995; vol. 12
References_xml – year: 1971
  ident: br0050
  article-title: Algebraic theory of automata
  contributor:
    fullname: Henneman
– year: 2009
  ident: br0100
  article-title: Elements of Automata Theory
  contributor:
    fullname: Sakarovitch
– volume: 10
  start-page: 385
  year: 1963
  end-page: 397
  ident: br0010
  article-title: Transition graphs and the star-height of regular events
  publication-title: Michigan Math. J.
  contributor:
    fullname: Eggan
– year: 1976
  ident: br0030
  article-title: Automata, Languages and Machines, vol. B
  contributor:
    fullname: Eilenberg
– volume: vol. 349
  start-page: 458
  year: 1989
  end-page: 467
  ident: br0080
  article-title: New results on the generalized star-height problem
  publication-title: STACS 89
  contributor:
    fullname: Therien
– year: 1974
  ident: br0020
  article-title: Automata, Languages and Machines, vol. A
  contributor:
    fullname: Eilenberg
– volume: 101
  start-page: 219
  year: 1992
  end-page: 250
  ident: br0090
  article-title: Some results on the generalized star-height problem
  publication-title: Inform. and Comput.
  contributor:
    fullname: Thérien
– year: 1986
  ident: br0070
  article-title: Varieties of Formal Languages
  contributor:
    fullname: Pin
– volume: vol. 12
  year: 1995
  ident: br0060
  article-title: Fundamentals of Semigroup Theory
  publication-title: London Mathematical Society Monographs. New Series
  contributor:
    fullname: Howie
– volume: 27
  start-page: 101
  year: 1983
  end-page: 115
  ident: br0040
  article-title: Representation theorems on regular languages
  publication-title: J. Comput. System Sci.
  contributor:
    fullname: Hashiguchi
– volume: vol. 12
  year: 1995
  ident: 10.1016/j.tcs.2016.09.024_br0060
  article-title: Fundamentals of Semigroup Theory
  contributor:
    fullname: Howie
– year: 1986
  ident: 10.1016/j.tcs.2016.09.024_br0070
  contributor:
    fullname: Pin
– volume: 101
  start-page: 219
  issue: 2
  year: 1992
  ident: 10.1016/j.tcs.2016.09.024_br0090
  article-title: Some results on the generalized star-height problem
  publication-title: Inform. and Comput.
  doi: 10.1016/0890-5401(92)90063-L
  contributor:
    fullname: Pin
– year: 2009
  ident: 10.1016/j.tcs.2016.09.024_br0100
  contributor:
    fullname: Sakarovitch
– volume: vol. 349
  start-page: 458
  year: 1989
  ident: 10.1016/j.tcs.2016.09.024_br0080
  article-title: New results on the generalized star-height problem
  contributor:
    fullname: Pin
– year: 1976
  ident: 10.1016/j.tcs.2016.09.024_br0030
  contributor:
    fullname: Eilenberg
– year: 1971
  ident: 10.1016/j.tcs.2016.09.024_br0050
  contributor:
    fullname: Henneman
– year: 1974
  ident: 10.1016/j.tcs.2016.09.024_br0020
  contributor:
    fullname: Eilenberg
– volume: 27
  start-page: 101
  year: 1983
  ident: 10.1016/j.tcs.2016.09.024_br0040
  article-title: Representation theorems on regular languages
  publication-title: J. Comput. System Sci.
  doi: 10.1016/0022-0000(83)90031-4
  contributor:
    fullname: Hashiguchi
– volume: 10
  start-page: 385
  year: 1963
  ident: 10.1016/j.tcs.2016.09.024_br0010
  article-title: Transition graphs and the star-height of regular events
  publication-title: Michigan Math. J.
  doi: 10.1307/mmj/1028998975
  contributor:
    fullname: Eggan
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SubjectTerms Alphabets
Combinatorial analysis
Group theory
Languages
Mathematical analysis
Rees matrix semigroup
Regular language
Star-height
Subword
Title On the star-height of subword counting languages and their relationship to Rees zero-matrix semigroups
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