Propositional dynamic logic of context-free programs

Abstract

The borderline between decidable and undecidable Propositional Dynamic Logic (PDL) is sought when iterative programs represented by regular expressions are augmented with increasingly more complex recursive programs represented by context-free languages. The results in this paper and its companion [HPS] indicate that this line is extremely close to the original regular PDL. The main result of the present paper is: The validity problem for PDL with additional programs αΔ(β)γΔ for regular α, β and γ, defined as Uiαi; β; γi, is Π11-complete. One of the results of [HPS] shows that the single program AΔ(B) AΔ for atomic A and B is actually sufficient for obtaining Π11- completeness. However, the proofs of this paper use different techniques which seem to be worthwhile in their own right.