A New Proof of Exponential Decidability for the Propositional -calculus with Program Converse

The propositional-Calculus (C) is a powerful propositional program logic with xpoints. C decidability with exponential upper bound was sketched for the rst time in 1988 by E. A. Emerson and Ch. S. Jutla on base of automata-theoretic technique, while a complete proof was published in 1999 only. Meanwhile M. Vardi sketched in 1998 an automata-theoretic proof of exponential decidability for the propositional-Calculus with program converse (C ?). We believe that alternative, independent and automata-free proofs of exponential decidabilities for C and for C ? are important for validation of these upper bounds and due to a complexity of automata-theoretic proofs. Previously the author published in 1997 a proof of exponential upper bound for C which exploited a so-called Program Schemata Technique (PST) for decidability of propo-sitional program logics. This time an extended PST is applied to C ? and yields exponential upper bound too.