Transition Invariants

  • Authors:
  • Andreas Podelski;Andrey Rybalchenko

  • Affiliations:
  • Max-Planck-Institut für Informatik, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany

  • Venue:
  • LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
  • Year:
  • 2004

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Abstract

Proof rules for program verification rely on auxiliary assertions. We propose a (sound and relatively complete) proof rule whose auxiliary assertions are transition invariants. A transition invariant of a program is a binary relation over program states that contains the transitive closure of the transition relation of the program. A relation is disjunctively well-founded if it is a finite union of well-founded relations. We characterize the validity of termination or another liveness property by the existence of a disjunctively well-founded transition invariant. The main contribution of our proof rule lies in its potential for automation via abstract interpretation.