Well-structured languages

Abstract This paper introduces the notion of well-structured language. A wellstructured 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 frequently studied in the field of computer-aided verification, where it has direct 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. In order to establish these 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 also allow us to strictly separate the expressive power of Petri net...

• Type: Journal
• Year: 2007
• Where: ACTA
• Authors: Gilles Geeraerts, Jean-François Raskin, Laurent Van Begin
• Keywords: ACTA 2007, Petri Nets, Transition Systems, Well-structured Languages