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)


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.


Commutation Relation Finite Automaton Canonical Morphism Free Monoid Commutative Monoids 
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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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