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A star-height problem in free monoids with partial commutations

  • Choffrut C. 
  • C. Duboc
Formal Languages And Automata
Part of the Lecture Notes in Computer Science book series (LNCS, volume 267)

Abstract

Let A be a finite alphabet and let ∼ be a congruence on the free monoid A* induced by a set of partial commutations θ=θR ⊂ AxA. It has been shown that if w ε A* contains all letters of A then [w*]={u ε A* | u ∼ wn for some n ≥ 0} is a rational set iff the graph of the complement \(\overline \theta\) of θ is connected. We prove: 1) if θ is not connected then [w*] has starheight one, 2) if θ and \(\overline \theta\) are connected there exist words w ε A* such that [w*] is a rational set of arbitrary starheight.

Keywords

Commutation Relation Finite Automaton Canonical Morphism Free Monoid Commutative Monoids 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Choffrut C. 
    • 1
  • C. Duboc
    • 1
  1. 1.Laboratoire d'Informatique de RouenUniversité de RouenMont-St-AignanFrance

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