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Applications of Time-Bounded Kolmogorov Complexity in Complexity Theory

Summary: Applications of Time-Bounded Kolmogorov
Complexity in Complexity Theory
Eric Allender?
Department of Computer Science
Rutgers University
New Brunswick, NJ 08903, USA
Abstract. This paper presents one method of using time-bounded Kol-
mogorovcomplexity as a measure of the complexity of sets, and outlines
a number of applications of this approach to di erent questions in com-
plexity theory. Connections will be drawn among the following topics:
NE predicates, ranking functions, pseudorandom generators, and hier-
archy theorems in circuit complexity.
1 Introduction
Complexitytheory provides a setting in which one can associate to any recursive
set L a function tL on the natural numbers, and with justi cation claim that
tL is a measure of the complexity of L; namely L can be accepted by exactly
those machines that run in time tLn. In this paper, we will consider a
means of using time-bounded Kolmogorov complexity to de ne a function KL,
that measures a di erent aspect of the complexity of L. We will argue that this


Source: Allender, Eric - Department of Computer Science, Rutgers University


Collections: Computer Technologies and Information Sciences