Relative Completeness of Abstraction Refinement for Software Model Checking

  • Authors:
  • Thomas Ball;Andreas Podelski;Sriram K. Rajamani

  • Affiliations:
  • -;-;-

  • Venue:
  • TACAS '02 Proceedings of the 8th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
  • Year:
  • 2002

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Abstract

Automated methods for an undecidable class of verification problems cannot be complete (terminate for every correct program). We therefore consider a new kind of quality measure for such methods, which is completeness relative to a (powerful but unrealistic) oraclebased method. More precisely, we ask whether an often implemented method known as "software model checking with abstraction refinement" is complete relative to fixpoint iteration with "oracle-guided" widening. We show that whenever backward fixpoint iteration with oracle-guided widening succeeds in proving a property 驴 (for some sequence of widenings determined by the oracle) then software model checking with a particular form of backward refinement will succeed in proving 驴. Intuitively, this means that the use of fixpoint iteration over abstractions and a particular backwards refinement of the abstractions has the effect of exploring the entire state space of all possible sequences of widenings.