A New Approximate Min-Max Theorem with Applications in Cryptography

TL;DR

This paper introduces a new proof technique that enhances the min-max theorem's application in computational complexity, enabling more efficient and elegant solutions for problems involving quantifier switching.

Contribution

It presents a novel proof method combining min-max theorem and convex approximation, providing quantitative improvements and simplifying proofs in complexity theory.

Findings

Enhanced min-max theorem applications in complexity problems

More concise and elegant proofs using the new technique

Quantitative improvements over traditional methods

Abstract

We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max theorem and convex approximation techniques, offering quantitative improvements over the standard way of using min-max theorems as well as more concise and elegant proofs.