Ferrante, Alessandro and Murano, Aniello and Parente, Mimmo - Enriched MU-Calculi Module Checking

lmcs:829 - Logical Methods in Computer Science, July 29, 2008, Volume 4, Issue 3
Enriched MU-Calculi Module Checking

Authors: Ferrante, Alessandro and Murano, Aniello and Parente, Mimmo

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 \mu-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 \mu-calculus module checking is solvable in exponential time, while hybrid graded \mu-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 \mu-calculus enriched with inverse programs (Fully enriched \mu-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.

Source : oai:arXiv.org:0805.3462
DOI : 10.2168/LMCS-4(3:1)2008
Volume: Volume 4, Issue 3
Published on: July 29, 2008
Submitted on: September 24, 2007
Keywords: Computer Science - Logic in Computer Science,F.1.1,F.1.2,F.3.1,D.2.4


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