A purely algebraic proof of McNaughton's theorem on infinite words

  • Bertrand Le Saec
  • Jean-Eric Pin
  • Pascal Weil
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 560)


We give a new, purely algebraic proof of McNaughton's theorem on infinite words, which states that each recognizable set X of infinite words can be recognized by a deterministic Muller automaton. Our proof uses the semigroup approach to recognizability and relies on certain algebraic properties of finite semigroups. It also provides a simple solution to the problem of finding a deterministic automaton for X when one is given a semigroup recognizing X.


Finite Automaton Testable Language Finite Semigroup Algebraic Proof Deterministic Automaton 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Bertrand Le Saec
    • 1
  • Jean-Eric Pin
    • 2
  • Pascal Weil
    • 2
  1. 1.LaBRIUniversité Bordeaux ITalence CedexFrance
  2. 2.Institut Blaise PascalLITP-CNRSParis Cedex 05France

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