Local abstraction-refinement for the μ-calculus

Harald Fecher, Sharon Shoham

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)289-306
Number of pages18
JournalInternational Journal on Software Tools for Technology Transfer
Issue number4
StatePublished - Aug 2011
Externally publishedYes


  • 3-valued abstraction
  • Model checking
  • Refinement
  • μ-calculus


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