Complexity Optimal Decision Procedure for a Propositional Dynamic Logic with Parallel Composition

PPDL det extends propositional dynamic logic (PDL) with parallel composition of programs. This new construct has separation semantics: to execute the parallel program (α||β) the initial state is separated into two substates and the programs α and β are executed on these substates. By adapting the elimination of Hintikka sets procedure, we provide a decision procedure for the satisfiability problem of PPDL det. We prove that this decision procedure can be executed in deterministic exponential time, hence that the satisfiability problem of PPDL det is EXPTIME-complete