The Propositional Dynamic Logic of Deterministic, Well-Structured Programs

Abstract

We consider a restricted propositional dynamic logic, Strict Deterministic Propositional Dynamic Logic (SDPDL), which is appropriate for reasoning about deterministic well-structured programs. In contrast to PDL, for which the validity problem is known to be complete in deterministic exponential time, the validity problem for SDPDL is shown to be polynomial space complete. We also show that SDPDL is less expensive than PDL. The results rely on structure theorems for models of satifiable SDPDL formulas, and the proods give insight into the effects of nondeterminism on intractability and expressiveness in program logics.