The mu-calculus and Model Checking [chapter]

Julian Bradfield, Igor Walukiewicz
<span title="">2018</span> <i title="Springer International Publishing"> Handbook of Model Checking </i> &nbsp;
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
more &raquo; ... 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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1007/978-3-319-10575-8_26</a> <a target="_blank" rel="external noopener" href="">fatcat:7adhegoggvcjthaa5x5uhfpt24</a> </span>
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