A Satisfiability Algorithm For The Mu-Calculus For Trees With Presburger Constraints

The μ-calculus is an expressive modal logic with fixed-point operators, well-known as a formal language to specify and verify labeled transition systems. We describe a satisfiability algorithm for the μ-calculus interpreted on tree models and extended with converse modalities and Presburger arithmetic operators. Converse modalities, together with the fixed-point operators, can be used to specify multi-directional and recursive properties in tree models. Presburger operators constrain the number of children nodes on tree models with respect to arithmetic expressions. The algorithm is based on a breadth-first search in a Fischer-Lardner construction of tree models. We also describe an implementation of the algorithm and report several experiments.