Abstract
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.
Research on this paper was partially supported by PRC “Mathématiques et Informatique” ESPRIT-BRA working group ASMICS.
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Le Saec, B., Pin, JE., Weil, P. (1991). A purely algebraic proof of McNaughton's theorem on infinite words. In: Biswas, S., Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1991. Lecture Notes in Computer Science, vol 560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54967-6_66
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DOI: https://doi.org/10.1007/3-540-54967-6_66
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