Policy Iteration within Logico-Numerical Abstract Domains

  • Pascal Sotin
  • Bertrand Jeannet
  • Franck Védrine
  • Eric Goubault
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6996)

Abstract

Policy Iteration is an algorithm for the exact solving of optimization and game theory problems, formulated as equations on min max affine expressions. It has been shown that the problem of finding the least fixpoint of semantic equations on some abstract domains can be reduced to such optimization problems. This enables the use of Policy Iteration to solve such equations, instead of the traditional Kleene iteration that performs approximations to ensure convergence.

We first show in this paper that the concept of Policy Iteration can be integrated into numerical abstract domains in a generic way. This allows to widen considerably its applicability in static analysis. We then consider the verification of programs manipulating Boolean and numerical variables, and we provide an efficient method to integrate the concept of policy in a logico-numerical abstract domain that mixes Boolean and numerical properties. Our experiments show the benefit of our approach compared to a naive application of Policy Iteration to such programs.

Keywords

Boolean Variable Stochastic Game Abstract Interpretation Concurrent Program Disjunctive Normal Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Pascal Sotin
    • 1
  • Bertrand Jeannet
    • 1
  • Franck Védrine
    • 2
  • Eric Goubault
    • 2
  1. 1.INRIAFrance
  2. 2.CEA-LIST LMeASIFrance

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