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VOLUME 4, ISSUE 3, PAPER 1


Enriched μ-Calculi Module Checking

©Ferrante Alessandro, Universita' di Salerno
©Aniello Murano, Universita' di Napoli
©Mimmo Parente, Universita' di Salerno

Abstract
The model checking problem for open systems has been intensively studied in the literature, for both finite-state (module checking) and infinite-state (pushdown module checking) systems, with respect to Ctl and Ctl*. In this paper, we further investigate this problem with respect to the μ-calculus enriched with nominals and graded modalities (hybrid graded Mu-calculus), in both the finite-state and infinite-state settings. Using an automata-theoretic approach, we show that hybrid graded μ-calculus module checking is solvable in exponential time, while hybrid graded μ-calculus pushdown module checking is solvable in double-exponential time. These results are also tight since they match the known lower bounds for Ctl. We also investigate the module checking problem with respect to the hybrid graded μ-calculus enriched with inverse programs (Fully enriched μ-calculus): by showing a reduction from the domino problem, we show its undecidability. We conclude with a short overview of the model checking problem for the Fully enriched Mu-calculus and the fragments obtained by dropping at least one of the additional constructs.

Publication date: July 30, 2008

Full Text: PDF | PostScript
DOI: 10.2168/LMCS-4(3:1)2008

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