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Mathematical systems theory

, Volume 18, Issue 1, pp 19–32 | Cite as

On the usefulness of bifaithful rational cones

  • Michel Latteux
  • Jeannine Leguy
Article

Abstract

Roughly, a faithful (resp. bifaithful) rational transduction is a non deterministic finite state mapping that does not decrease (resp. alter) the length of words by very much. We introduce the notion of stronglyf-saturated language:L is stronglyf-saturated if and only if for any languageL′, from which we can obtainL by faithful rational transduction, for any languageL″, image ofL by a faithful rational transduction, there exists a bifaithful rational transduction τ such thatL″ is the image ofL′ τ. We prove that no quasirational language and no language in the substitution closed rational cone generated by bounded languages is stronglyf-saturated. Conversely, we establish that a language such as\(\bar D_1^{\prime *} = \{ w \in \{ a,b\} ^* /|w|_a \ne |w|_b \}\), very low in the hierarchy of algebraic languages, is stronglyf-saturated thus is not a quasirational language. We also establish that any commutative quasi rational language over two letters is rational.

Keywords

Computational Mathematic State Mapping Rational Cone Rational Language Algebraic Language 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc 1985

Authors and Affiliations

  • Michel Latteux
    • 1
  • Jeannine Leguy
    • 1
  1. 1.Laboratoire de Recherche en Informatique FondamentaleFrance

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