The theory of WSTS: the case of complete WSTS

  • Authors:
  • Alain Finkel;Jean Goubault-Larrecq

  • Affiliations:
  • ENS Cachan, France;ENS Cachan, France

  • Venue:
  • PETRI NETS'12 Proceedings of the 33rd international conference on Application and Theory of Petri Nets
  • Year:
  • 2012

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Abstract

We describe a simple, conceptual forward analysis procedure for ∞-complete WSTS $\mathfrak S$. This computes the so-called clover of a state. When $\mathfrak S$ is the completion of a WSTS $\mathfrak X$, the clover in $\mathfrak S$ is a finite description of the downward closure of the reachability set. We show that such completions are ∞-complete exactly when $\mathfrak X$ is an ω2-WSTS, a new robust class of WSTS. We show that our procedure terminates in more cases than the generalized Karp-Miller procedure on extensions of Petri nets. We characterize the WSTS where our procedure terminates as those that are clover-flattable. Finally, we apply this to well-structured Presburger counter systems.