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Reports (Technical Report) Year : 2010

Equational Abstraction Refinement for Certified Tree Regular Model Checking

Abstract

Tree Regular Model Checking (TRMC) is the name of a family of techniques for analyzing in nite-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 nite time. This paper proposes a new CounterExample Guided Abstraction Re- nement (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 nite time. This set is represented by R=E-automata, a new extended tree automaton formalism whose structure can be exploited to detect and remove false positives in an e cient 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 certi- ed by Coq, which means that they are formally proved correct.
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Dates and versions

inria-00501487 , version 1 (12-07-2010)
inria-00501487 , version 2 (11-05-2012)

Identifiers

  • HAL Id : inria-00501487 , version 2

Cite

Yohan Boichut, Benoît Boyer, Thomas Genet, Axel Legay. Equational Abstraction Refinement for Certified Tree Regular Model Checking. [Technical Report] 2010. ⟨inria-00501487v2⟩
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