Relativization of the Theory of Computational Complexity

Abstract

Blum's machine-independent treatment of the complexity of partial recursive functions is extended to relative algorithms (as represented by Turing machines with oracles). We prove relativizations of several results of Blum complexity theory, such as the compression theorem. A recursive relatedness theorem is proved, showing that any two relative complexity measures are related by fixed recursive function. This theorem allows us to obtain proofs of results for all measures from proofs for a particular measure.