Formal Language Constrained Reachability and Model Checking Propositional Dynamic Logics

Abstract. We show interreducibility under (Turing) reductions of low polynomial degree between three families of problems parametrised by classes of formal languages: the problem of reachability in a directed graph constrained by a formal language, the problem of deciding whether or not the intersection of a language of some class with a regular language is empty, and the model checking problem for Propositional Dynamic Logic over some class of formal languages. This allows several decidability and complexity results to be transferred, mainly from the area of formal languages to the areas of modal logics and formal language constrained reachability.