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Well-structured languages

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Abstract

This paper introduces the notion of well-structured language. A well-structured language can be defined by a labelled well-structured transition system, equipped with an upward-closed set of accepting states. That peculiar class of transition systems has been extensively studied in the field of computer-aided verification, where it has direct an important applications. Petri nets, and their monotonic extensions (like Petri nets with non-blocking arcs or Petri nets with transfer arcs), for instance, are special subclasses of well-structured transition systems. We show that the class of well-structured languages enjoy several important closure properties. We propose several pumping lemmata that are applicable respectively to the whole class of well-structured languages and to the classes of languages recognized by Petri nets or Petri nets with non-blocking arcs. These pumping lemmata allow us to characterize the limits in the expressiveness of these classes of language. Furthermore, we exploit the pumping lemmata to strictly separate the expressive power of Petri nets, Petri nets with non-blocking arcs and Petri nets with transfer arcs.

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Authors and Affiliations

  1. Département d’Informatique, Université Libre de Bruxelles, CPI 212, Boulevard du Triomphe, 1050, Bruxelles, Belgium

    Gilles Geeraerts, Jean-François Raskin & Laurent Van Begin

Authors
  1. Gilles Geeraerts
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  2. Jean-François Raskin
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  3. Laurent Van Begin
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Correspondence to Gilles Geeraerts.

Additional information

Laurent Van Begin has been supported by a “First Europe” grant EPH3310300R0012 of the Walloon Region. This work has been partially supported by a FRFC grant number 2.4530.02 of the belgian National Fund for Scientific Research (FNRS).

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Geeraerts, G., Raskin, JF. & Van Begin, L. Well-structured languages. Acta Informatica 44, 249–288 (2007). https://doi.org/10.1007/s00236-007-0050-3

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