Equational abstraction refinement for certified tree regular model checking

  • Authors:

  • Yohan Boichut;Benoit Boyer;Thomas Genet;Axel Legay

  • Affiliations:

  • LIFO, Université Orléans, France;VERIMAG, Université Joseph Fourier, France;IRISA, Université Rennes 1, France;INRIA, Rennes, France

  • Venue:
  • ICFEM'12 Proceedings of the 14th international conference on Formal Engineering Methods: formal methods and software engineering
  • Year:
  • 2012

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Abstract

Tree Regular Model Checking (TRMC) is the name of a family of techniques for analyzing infinite-state systems in which states are represented by trees and sets of states by tree automata. The central problem is to decide whether a set of bad states belongs to the set of reachable states. An obstacle is that this set is in general neither regular nor computable in finite time. This paper proposes a new CounterExample Guided Abstraction Refinement (CEGAR) algorithm for TRMC. Our approach relies on a new equational-abstraction based completion algorithm to compute a regular overapproximation of the set of reachable states in finite time. This set is represented by $\mathcal{R}_{/E}$-automata, a new extended tree automaton formalism whose structure can be exploited to detect and remove false positives in an efficient manner. Our approach has been implemented in TimbukCEGAR, a new toolset that is capable of analyzing Java programs by exploiting an elegant translation from the Java byte code to term rewriting systems. Experiments show that TimbukCEGAR outperforms existing CEGAR-based completion algorithms. Contrary to existing TRMC toolsets, the answers provided by TimbukCEGAR are certified by Coq, which means that they are formally proved correct.