Notes on Levin's Theory of Average-Case Complexity
نویسنده
چکیده
In 1984, Leonid Levin initiated a theory of average-case complexity. We provide an exposition of the basic definitions suggested by Levin, and discuss some of the considerations underlying these definitions.
منابع مشابه
Average Time Complexity
We extend Levin's theory of average polynomial time to arbitrary time-bounds in accordance with the following general principles: (1) It essentially agrees with Levin's notion when applied to polynomial time-bounds. (2) If a language L belongs to DTIME(T(n)), for some time-bound T (n), then every distributional problem (L;) is T on the-average. (3) If L does not belong to DTIME(T(n)) almost eve...
متن کاملAverage Time Complexity Classes
We extend Levin's theory of average polynomial time to arbitrary time bounds and prove that average time complexity classes form as ne a hierarchy as do deterministic time complexity classes.
متن کاملA Survey
The purpose of this manuscript is to prov\de a survey to basic notions and results concerning a theory of average case complexity initiated by Leonid Levin. This survey is mainly bas~d on Levin's paper Avet:age Case Complete Problems [L], and expositions of it due to Johnson [J], Gurevich [GJ, and Gurevich and McCauley [GMc]. Further developments due to Gurevich [GJ and others are also briefly ...
متن کاملNotes for Lecture 8
In these notes we introduce Levin’s theory of average-case complexity. This theory is still in its infancy: in these notes we will introduce the notion of “distributional problems,” discuss various formalizations of the notion of “algorithms that are efficient on average,” introduce a reducibility that preserves efficient average-case solvability. Next time we will prove that there is a problem...
متن کاملAverage Case Complexity, Revisited
More than two decades elapsed since Levin set forth a theory of average-case complexity. In this survey we present the basic aspects of this theory as well as some of the main results regarding it. The current presentation deviates from our old “Notes on Levin’s Theory of Average-Case Complexity” (ECCC, TR97-058, 1997) in several aspects.
متن کامل