Resource-Bounded Kolmogorov Complexity Revisited

Resource-Bounded Kolmogorov Complexity Revisited

We take a fresh look at CD complexity, where CD t (x) is the smallest program that distinguishes x from all other strings in time t(jxj). We also look at a CND complexity, a new nondeterministic variant of CD complexity. We show several results relating time-bounded C, CD and CND complexity and their applications to a variety of questions in computational complexity theory including: Showing ho...

Resour e-Bounded Kolmogorov Complexity Revisited

Time - Bounded Kolmogorov Complexity in Complexity Theory

This paper presents one method of using time-bounded Kol-mogorov complexity as a measure of the complexity of sets, and outlines a number of applications of this approach to diierent questions in complexity theory. Connections will be drawn among the following topics: NE predicates, ranking functions, pseudorandom generators, and hierarchy theorems in circuit complexity.

The pervasive reach of resource-bounded Kolmogorov complexity in computational complexity theory

We continue an investigation into resource-bounded Kolmogorov complexity [ABK06], which highlights the close connections between circuit complexity and Levin’s time-bounded Kolmogorov complexity measure Kt (and other measures with a similar flavor), and also exploits derandomization techniques to provide new insights regarding Kolmogorov complexity. The Kolmogorov measures that have been introd...

Bounded Kolmogorov Complexity Based on Cognitive Models

Computable versions of Kolmogorov complexity have been used in the context of pattern discovery [1]. However, these complexity measures do not take the psychological dimension of pattern discovery into account. We propose a method for pattern discovery based on a version of Kolmogorov complexity where computations are restricted to a cognitive model with limited computational resources. The pot...