Lecture Notes in Computer Science Volume 582, 1992, pp 1-19
Date: 30 May 2005

Model checking and boolean graphs

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This paper describes a method for translating a satisfaction problem of the modal μ-calculus into a problem of finding a certain marking of a boolean graph. By giving algorithms to solve the graph problem, we present a global model checking algorithm for the modal μ-calculus of alternation depth one, which has time-complexity ¦A¦¦T¦, where ¦A¦ is the size of the assertion and ¦T¦ is the size of the model (a labelled transition system). This algorithm extends to an algorithm for the full modal μ-calculus which runs in time (¦A¦¦T¦)ad, where ad is the alternation depth, improving on earlier presented algorithms. Moreover, a local algorithm is presented for alternation depth one, which runs in time ¦A¦¦T¦log(¦A¦¦T¦), improving on the earlier published algorithms that are all at least exponential.

This work is supported by the ESPRIT Basic Research Action CEDISYS and by the Danish Natural Science Research Council.