Derandomization under Different Resource Constraints

TL;DR

This paper explores the tradeoffs in derandomization under resource constraints, providing new proofs and demonstrating how probabilistic existence results relate to Kolmogorov complexity bounds.

Contribution

It introduces a resource-bounded version of the EL Theorem and applies it to derive three instances of resource-bounded derandomization, linking probabilistic methods to complexity bounds.

Findings

Proved a resource-bounded EL Theorem.

Established tradeoffs between codebook compressibility and capacity.

Demonstrated derandomization results under resource constraints.

Abstract

We provide another proof to the EL Theorem. We show the tradeoff between compressibility of codebooks and their communication capacity. A resource bounded version of the EL Theorem is proven. This is used to prove three instances of resource bounded derandomization. This paper is in support of the general claim that if the existence of an object can be proven with the probabilistic method, then bounds on its Kolmogorov complexity can be proven as well.