A decidable mu-calculus: Preliminary report

Abstract

We describe a mu-calculus which amounts to modal logic plus a minimization operator, and show that its satisfiability problem is decidable in exponential time. This result subsumes corresponding results for propositional dynamic logic with test and converse, thus supplying a better setting for those results. It also encompasses similar results for a logic of flowgraphs. This work provides an intimate link between PDL as defined by the Segerberg axioms and the mu-calculi of de Bakker and Park.