Inferring definite counterexamples through under-approximation

  • Authors:
  • Jörg Brauer;Axel Simon

  • Affiliations:
  • Embedded Software Laboratory, RWTH Aachen University, Germany;Informatik 2, Technical University Munich, Germany

  • Venue:
  • NFM'12 Proceedings of the 4th international conference on NASA Formal Methods
  • Year:
  • 2012

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Abstract

Abstract interpretation for proving safety properties summarizes concrete traces into abstract states, thereby trading the ability to distinguish traces for tractability. Given a violation of a safety property, it is thus unclear which trace led to the violation. Moreover, since part of the abstract state is over-approximate, such a trace may not exist at all. We propose a novel backward analysis that is based on abduction of propositional Boolean logic and that only generates legitimate traces that reveal actual defects. The key to tractability lies in modifying an existing projection algorithm to stop prematurely with an under-approximation and by combining various algorithmic techniques to handle loops finitely.