A Decidable Non-Regular Modal Fixpoint Logic

Florian Bruse, Martin Lange

Abstract: Fixpoint Logic with Chop (FLC) extends the modal μ-calculus with an operator for sequential composition between predicate transformers. This makes it an expressive modal fixpoint logic which is capable of formalising many non-regular program properties. Its satisfiability problem is highly undecidable. Here we define Visibly Pushdown Fixpoint Logic with Chop, a fragment in which fixpoint formulas are required to be of a certain form resembling visibly pushdown grammars. We give a sound and complete game-theoretic characterisation of FLC’s satisfiability problem and show that the games corresponding to formulas from this fragment are stair-parity games and therefore effectively solvable, resulting in 2EXPTIME-completeness of this fragment. The lower bound is inherited from PDL over Recursive Programs, which is structurally similar but considerably weaker in expressive power.