Kolmogorov Complexity, Complexity Cores, and the Distribution of Hardness F
نویسندگان
چکیده
Problems that are complete for exponential space are prov-ably intractable and known to be exceedingly complex in several technical respects. However, every problem decidable in exponential space is eeciently reducible to every complete problem, so each complete problem must have a highly organized structure. The authors have recently exploited this fact to prove that complete problems are, in two respects, unusually simple for problems in expontential space. Speciically, every complete problem must have ususually small complexity cores and unusually low space-bounded Kolmogorov complexity. It follows that the complete problems form a negligibly small subclass of the problems de-cidable in exponential space. This paper explains the main ideas of this work.
منابع مشابه
Kolmogorv Complexity, Complexity Cores, and the Distribution of Hardness
Every language that is P m -hard for ESPACE is shown to have unusually small complexity cores and unusually low space-bounded Kolmogorov complexity. It follows that the Pm-complete languages form a measure 0 subset of ESPACE.
متن کاملKolmogorov Complexity Complexity Cores and the Distribution of Hardness
Problems that are complete for exponential space are prov ably intractable and known to be exceedingly complex in several techni cal respects However every problem decidable in exponential space is e ciently reducible to every complete problem so each complete prob lem must have a highly organized structure The authors have recently exploited this fact to prove that complete problems are in two...
متن کامل3D Scene and Object Classification Based on Information Complexity of Depth Data
In this paper the problem of 3D scene and object classification from depth data is addressed. In contrast to high-dimensional feature-based representation, the depth data is described in a low dimensional space. In order to remedy the curse of dimensionality problem, the depth data is described by a sparse model over a learned dictionary. Exploiting the algorithmic information theory, a new def...
متن کاملTime-Bounded Universal Distributions
We show that under a reasonable hardness assumptions, the time-bounded Kolmogorov distribution is a universal samplable distribution. Under the same assumption we exactly characterize the worst-case running time of languages that are in average polynomial-time over all P-samplable distributions.
متن کاملNew Insights on the (Non-)Hardness of Circuit Minimization and Related Problems
The Minimum Circuit Size Problem (MCSP) and a related problem (MKTP) that deals with time-bounded Kolmogorov complexity are prominent candidates for NP-intermediate status. We show that, under very modest cryptographic assumptions (such as the existence of one-way functions), the problem of approximating the minimum circuit size (or time-bounded Kolmogorov complexity) within a factor of n1−o(1)...
متن کامل