Mathematical systems theory

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

On the usefulness of bifaithful rational cones

  • Michel Latteux
  • Jeannine Leguy


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.


Computational Mathematic State Mapping Rational Cone Rational Language Algebraic Language 
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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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