Games with Second-order Quantiiers Which Decide Propositional Program Logics

The paper demonstrates how second-order quantiication and nite games can be exploited for deciding complicated propositional program logics like the propositional-Calculus with converse (C ?). This approach yields a new proof that C ? is in EXP T IME. Automata-theoretic technique is a very powerful and popular approach for deciding complicated propositional program logics 19, 20, 3]. The rst paper 19] has studied elementary decidability of Propositional Dynamic Logic of looping and converse ((PDL ?). The next paper 20] has established elementary decidability and nite model property for the propositional-Calculus (C). The last paper 3] has proved exponential decidability for this logic. Recently (in 1998) this approach yielded exponential decidability for the proposi-tional-Calculus with program converse (C ?) 21] { a logic which amalgamates PDL ? and C. Basically, automata-theoretic approach comprises two stages: rst, a reduction of the decidability problem for a particular logic to the emptiness problem for a particular class of automata, and then application of a direct decision procedure for this emptiness problem. A self-contained presentation of an alternative automata-free game-theoretic approach for deciding propositional program logics is the main topic of the paper. It includes: While on leave from A.P.