Forward Analysis for WSTS, Part II: Complete WSTS

  • Authors:
  • Alain Finkel;Jean Goubault-Larrecq

  • Affiliations:
  • LSV, ENS Cachan, CNRS, France;LSV, ENS Cachan, CNRS, France and INRIA Saclay, France

  • Venue:
  • ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
  • Year:
  • 2009

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Abstract

We describe a simple, conceptual forward analysis procedure for ***-complete WSTS $\mathfrak S$. This computes the clover of a state s 0 , i.e., a finite description of the closure of the cover of s 0 . When $\mathfrak S$ is the completion of a WSTS $\mathfrak X$, the clover in $\mathfrak S$ is a finite description of the cover in $\mathfrak X$. We show that this applies exactly when $\mathfrak X$ is an *** 2 -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 counter systems.