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Rational index of Vector Addition Systems languages

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Summary

The rational index ρL of a non-empty language L is a function of ℕ into ℕ, whose asymptotic behavior can be used to classify languages. We prove that the languages associated to Vector Addition System or Petri nets have rational indexes bounded by polynomials. This situation should be contrasted with the case of context-free languages. Indeed some context-free languages like the Greibach's languages have rational indexes bounded by polynomials. But some other context-free languages have rational indexes in exp Θ n and the generators of the rational cone of context-free languages have rational indexes in exp Θ n 2/ln n. We give an upper bound and a lower bound on the rational index of each term of an infinite sequence of V.A.S. languages, such that any V.A.S. language can be obtained as the image by a rational transduction of one of these languages.

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Authors and Affiliations

  1. Université de Paris X Nanterre, Nanterre, France

    Laurent Pierre

  2. L.I.T.P., 4 Place Jussieu, Paris, France

    Laurent Pierre

  3. SYSECA T.R., 315 Bureaux de la Colline, F-92213, Saint-Cloud Cedex, France

    Sylviane R. Schwer

Authors
  1. Laurent Pierre
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  2. Sylviane R. Schwer
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Pierre, L., Schwer, S.R. Rational index of Vector Addition Systems languages. Acta Informatica 26, 503–525 (1989). https://doi.org/10.1007/BF00263577

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  • DOI: https://doi.org/10.1007/BF00263577

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