Applications of Time-Bounded Kolmogorov Complexity in Complexity Theory
نویسنده
چکیده
This paper presents one method of using time-bounded Kolmogorov complexity as a measure of the complexity of sets, and outlines a number of applications of this approach to di erent questions in complexity theory. Connections will be drawn among the following topics: NE predicates, ranking functions, pseudorandom generators, and hierarchy theorems in circuit complexity.
منابع مشابه
Universal distributions and time - boundedKolmogorov
The equivalence of universal measure, a priori probability and the negative exponential of Kolmogorov complexity is a well known result with signiicance both to the theory of Kolmogorov complexity and many of its applications. In this paper we consider deenitions for the time-bounded setting where similar equivalences hold. Unlike the unbounded case, time-bounded universal distributions give ri...
متن کاملTime - 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.
متن کاملThe 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...
متن کاملOn Languages with Very High Information Content
The main result of this paper is the following: Any language in ESPACE that is bounded truthtable reducible in polynomial time to a set with very high space-bounded Kolmogorov complexity must be bounded truth-table reducible in polynomial time to a sparse set.
متن کاملResource-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...
متن کامل