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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Enriched μ-Calculi Module Checking
verfasst von : Alessandro Ferrante, Aniello Murano
Erschienen in: Foundations of Software Science and Computational Structures
Verlag: Springer Berlin Heidelberg
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The model checking problem for open finite-state systems (called
module checking
) has been intensively studied in the literature with respect to
CTL
and
CTL
*
. In this paper, we focus on module checking with respect to the
fully enriched μ
-calculus
and some of its fragments. Fully enriched
μ
-calculus is the extension of the propositional
μ
-calculus with
inverse programs
,
graded modalities
, and
nominals
. The fragments we consider here are obtained by dropping at least one of the additional constructs. For the full calculus, we show that module checking is undecidable by using a reduction from the domino problem. For its fragments, instead, we show that module checking is decidable and
ExpTime
-complete. This result is obtained by using, for the upper bound, a classical automata-theoretic approach via
Forest Enriched Automata
and, for the lower bound, a reduction from the module checking problem for
CTL
, known to be
ExpTime
-hard.