Some Relationships Between Logics of Programs and Complexity Theory

Abstract We show that some open problems concerning comparative schematology and logics of programs are equivalent to open problems in complexity theory. In particular, we show that P SPACE =P TIME holds if and only if flow-diagrams with arrays are of the same computational power as recursive procedures. Both conditions are equivalent to the statement that programming logics based on the mentioned classes of program schemes have equal expressive power. A similar characterization is given for some other equalities between complexity classes.

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