Acta Informatica

, Volume 44, Issue 3–4, pp 249–288 | Cite as

Well-structured languages

  • Gilles Geeraerts
  • Jean-François Raskin
  • Laurent Van Begin
Original article


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.


Expressive Power Regular Language Monotonic Extension Emptiness Problem Arbitrary Homomorphism 
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 2007

Authors and Affiliations

  • Gilles Geeraerts
    • 1
  • Jean-François Raskin
    • 1
  • Laurent Van Begin
    • 1
  1. 1.Département d’InformatiqueUniversité Libre de BruxellesBruxellesBelgium

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