On Baker-Gill-Solovay Oracle Turing Machines and Relativization Barrier

TL;DR

This paper examines the relativization barrier in computational complexity, demonstrating that diagonalization remains a valid proof technique but has specific prerequisites when applied to oracle Turing machines.

Contribution

It clarifies the role of diagonalization in relativization and its limitations concerning the relativization barrier in complexity theory.

Findings

Diagonalization is a valid proof technique with certain prerequisites.

The relativization barrier has nuanced implications for proof methods.

The work refines understanding of oracle Turing machines and complexity class separations.

Abstract

This work analyses the so-called "Relativization Barrier" with respect to the Baker-Gill-Solovay oracle Turing machine. We show that the {\em diagonalization} technique is a valid mathematical proof technique, but it has some prerequisites when referring to the "relativization barrier."