Model-Checking the Higher-Dimensional Modal mu-Calculus

Martin Lange
(School of Electrical Engineering and Computer Science, University of Kassel, Germany)
Etienne Lozes
(School of Electrical Engineering and Computer Science, University of Kassel, Germany)

The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in polynomial time, and conversely every polynomial-time decidable problem that has a bisimulation-invariant encoding into labeled transition systems can also be defined in the higher-dimensional modal mu-calculus. We exemplify the latter connection by giving several examples of decision problems which reduce to model checking of the higher-dimensional modal mu-calculus for some fixed formulas. This way generic model checking algorithms for the logic can then be used via partial evaluation in order to obtain algorithms for theses problems which may benefit from improvements that are well-established in the field of program verification, namely on-the-fly and symbolic techniques. The aim of this work is to extend such techniques to other fields as well, here exemplarily done for process equivalences, automata theory, parsing, string problems, and games.

In Dale Miller and Zoltán Ésik: Proceedings 8th Workshop on Fixed Points in Computer Science (FICS 2012), Tallinn, Estonia, 24th March 2012, Electronic Proceedings in Theoretical Computer Science 77, pp. 39–46.
Published: 14th February 2012.

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