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Local abstraction–refinement for the μ-calculus

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Abstract

A key technique for the verification of programs is counterexample-guided abstraction–refinement (CEGAR). Grumberg et al. (LNCS, vol 3385, pp. 233–249. Springer, Berlin, 2005; Inf Comput 205(8):1130–1148, 2007) developed a CEGAR-based algorithm for the modal μ-calculus. There, every abstract state is split in a refinement step. In this paper, the work of Grumberg et al. is generalized by presenting a new CEGAR-based algorithm for the μ-calculus. It is based on a more expressive abstract model and applies refinement only locally (at a single abstract state), i.e., the lazy abstraction technique for safety properties is adapted to the μ-calculus. Furthermore, it separates refinement determination from the (3-valued based) model checking. Three different heuristics for refinement determination are presented and illustrated.

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Authors and Affiliations

  1. Albert-Ludwigs-Universität Freiburg, Freiburg, Germany

    Harald Fecher

  2. The Technion, Haifa, Israel

    Sharon Shoham

Authors
  1. Harald Fecher
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  2. Sharon Shoham
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Correspondence to Sharon Shoham.

Additional information

A preliminary version of this work appeared in [12].

This paper belongs to the Special Section for SPIN 07. Its publication has been delayed for organizational reasons.

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Fecher, H., Shoham, S. Local abstraction–refinement for the μ-calculus. Int J Softw Tools Technol Transfer 13, 289–306 (2011). https://doi.org/10.1007/s10009-011-0202-1

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