Small witnesses for abstract interpretation-based proofs

  • Authors:
  • Frédéric Besson;Thomas Jensen;Tiphaine Turpin

  • Affiliations:
  • IRISA, Inria, CNRS, Université de Rennes 1, Rennes, France;IRISA, Inria, CNRS, Université de Rennes 1, Rennes, France;IRISA, Inria, CNRS, Université de Rennes 1, Rennes, France

  • Venue:
  • ESOP'07 Proceedings of the 16th European conference on Programming
  • Year:
  • 2007

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Abstract

Abstract interpretation-based proof carrying code uses post-fixpoints of abstract interpretations to witness that a program respects a safety policy. Some witnesses carry more information than needed and are therefore unnecessarily large. We introduce a notion of size of a witness and propose techniques for reducing the size of such certificates. For distributive analyses, we show that a smallest witness exist and we give an iterative algorithm for computing it. For nondistributive analyes we propose a technique for pruning a witness and illustrate this pruning on a relational, polyhedra-based analysis. Finally, only the existence of a witness is needed to assure the code consumer of the safety of a given program. This makes possible a compression technique of witnesses where only part of a witness is sent together with an encoding of the iterative steps necessary to prove that it is part of a post-fixpoint.