
TL;DR
This paper proves that PSPACE equals the 4th level of the polynomial hierarchy, using a novel approach involving skolemization, XOR analysis, and local polynomial-time procedures to establish the equivalence.
Contribution
It demonstrates that PSPACE is equal to the 4th level of the polynomial hierarchy, providing a new proof and implications for complexity theory.
Findings
PSPACE equals the 4th level of PH.
A polynomial-time method to analyze XOR dependencies.
Implications for relativization and oracle results.
Abstract
In this paper we show that PSPACE is equal to 4th level in the polynomial hierarchy. We also deduce a lot of important consequences. True quantified Boolean formula is a generalisation of the Boolean Satisfiability Problem, where determining of interpretation that satisfies a given Boolean formula is replaced by existence of Boolean functions that makes a given QBF to be tautology. Such functions are called the Skolem functions. The essential idea of the proof is to show that for any quantified Boolean formula we can obtain a formula which is in the 4th level of the polynomial hierarchy, no more than polynomial in the size of a given , such that the truth of can be determined from the truth of . The idea is to skolemize, and then use additional formulas from the 2nd level of the polynomial hierarchy inside the skolemized prefix to enforce that the…
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Taxonomy
TopicsFormal Methods in Verification · Logic, Reasoning, and Knowledge · Logic, programming, and type systems
