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Relations rationnelles infinitaires

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Abstract

In this paper, we build a theory of infinitary rational relations, which is an extension of the theory of finitary rational relations, i. e. sets ofK-vectors of finite words which are recognized by finite automata withK tapes, and at the same time an extension of the theory of infinitary rational languages, i.e., sets of finite and infinite words which are recognized by finite automata (the condition of recognizability of an infinite word is that its reading by the automaton must go through a state, wich belongs to a designated subset, infinitly time).

Our main result is a theorem similar to the Kleene theorem about rational languages of finite words: it is proved that the family of relations recognized by finite automata withK tapes is the family of relations obtained from the finite finitary relations with a finite sequence of operations of: union, product, finite star, and infinite star.

Then the closure properties of this family of relations, are studied.

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Authors and Affiliations

  1. Laboratoire d’Informatique Théorique et Programmation Université Paris 7, 2, Place Jussieu, 75221, Paris Cedex 05

    F. Gire & M. Nivat

Authors
  1. F. Gire
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  2. M. Nivat
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Gire, F., Nivat, M. Relations rationnelles infinitaires. Calcolo 21, 91–125 (1984). https://doi.org/10.1007/BF02575909

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  • DOI: https://doi.org/10.1007/BF02575909

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