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On rational solution of the state equation of a finite automaton

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  • R. Chaudhuri
  • H. Höft

Abstract

We prove that the necessary and sufficient condition for the state equation of a finite automaton M to have a rational solution is that the lexicographical Gödel numbers of the strings belonging to each of the end-sets of M form an ultimately periodic set. A method of determining the existence of a rational solution of the state equation is also given.

Suggested Citation

  • R. Chaudhuri & H. Höft, 1988. "On rational solution of the state equation of a finite automaton," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 11, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:602673
    DOI: 10.1155/S0161171288000420
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