The mu-calculus and Model Checking

Julian Bradfield , Igor Walukiewicz (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

This chapter presents a part of the theory of the mu-calculus that is relevant to the, broadly understood, model-checking problem. The mu-calculus is one of the most important logics in model-checking. It is a logic with an exceptional balance between expressiveness and algorithmic properties. The chapter describes in length the game characterization of the semantics of the mu-calculus. It discusses the theory of the mu-calculus starting with the tree model property, and bisimulation invariance. Then it develops the notion of modal automaton: an automaton-based model behind the mu-calculus. It gives a quite detailed explanation of the satisfiability algorithm, followed by the results on alternation hierarchy, proof systems, and interpolation. Finally, the chapter discusses the relations of the mu-calculus to monadic second-order logic as well as to some program and temporal logics. It also presents two extensions of the mu-calculus that allow us to address issues such as inverse modalities.

Domaines: Logique en informatique [cs.LO]

Julian Bradfield, Igor Walukiewicz. The mu-calculus and Model Checking. Handbook of Model Checking, Springer International Publishing, pp.871-919, 2018, ⟨10.1007/978-3-319-10575-8_26⟩. ⟨hal-02397703⟩