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Journal of Logic and Computation 2002 12(2):255-269; doi:10.1093/logcom/12.2.255
© 2002 by Oxford University Press
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Original Article

µ-Calculus with Explicit Points and Approximations

Mads Dam1 and Dilian Gurov2

1 Department of Microelectronics and Information Technology (IMIT), Royal Institute of Technology (KTH), Electrum 229, SE-164 40 Kista, Sweden. E-mail: mfd{at}it.kth.se 2 Swedish Institute of Computer Science (SICS), Box 1263, SE-164 29 Kista, Sweden. E-mail: dilian{at}sics.se

We present a Gentzen-style sequent calculus for program verification which accommodates both model checking-like verification based on global state space exploration, and compositional reasoning. To handle the complexities arising from the presence of fixed-point formulas, programs with dynamically evolving architecture, and cut rules we use transition assertions, and introduce fixed-point approximants explicitly into the assertion language. We address, in a game-based manner, the semantical basis of this approach, as it applies to the entailment subproblem. Soundness and completeness results are obtained, and examples are shown illustrating some of the concepts.

Keywords: µ-calculus; sequent calculus; program verification; compositionality

Received September 2000.


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