Model-Checking the Higher-Dimensional Modal mu-Calculus

Abstract

The higher-dimensional modal -calculus is an extension of the -calculus that has been introduced by Otto. The fascinating fea- ture of this extension is that it precisely characterizes the bisimulation- invariant polynomial-time properties over nite structures. In this paper we investigate how the model checking problem of the higher-dimensional modal -calculus can be eciently implemented. We propose two al- gorithms, based on extensions of local model checking and symbolic model checking algorithms respectively. We then illustrate the poten- tial strength of these generic algorithms for deciding specic problems of various elds, as process equivalences, automata theory, parsing, string problems, or games.