Some relationships between logics of programs and complexity theory

The aim of this paper is to show that some open problems in Comparative Schematology and in Logics of Programs are equivalent to open problems in Complexity Theory. In particular we show that PSPACE = PTIME holds if and only if flow-diagrams with arrays are of the same computational power as recursive procedures. These statements are also equivalent to the following statement: Logics based on the above-mentioned classes of program schemes have equal expressive power. A similar characterization may be given for other complexity classes.