期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2009
卷号：2009
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：We continue an investigation into resource-bounded Kolmogorov complexity \cite{abkmr}, 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 introduced have many advantages over other approaches to defining resource-bounded Kolmogorov complexity (such as much greater independence from the underlying choice of universal machine that is used to define the measure) [ABKMR]. Here, we study the properties of other measures that arise naturally in this framework. The motivation for introducing yet more notions of resource-bounded Kolmogorov complexity are two-fold: * to demonstrate that other complexity measures such as branching-program size and formula size can also be discussed in terms of Kolmogorov complexity, and * to demonstrate that notions such as nondeterministic Kolmogorov complexity and distinguishing complexity [BFL] also fit well into this framework. The main theorems that we provide using this new approach to resource-bounded Kolmogorov complexity are: * A complete set ( \RKNt ) for NEXP/poly defined in terms of strings of high Kolmogorov complexity. * A lower bound, showing that \RKNt is not in NP intersect coNP. * New conditions equivalent to the conditions ``NEXP is contained in nonuniform NC1'' and ``NEXP is contained in L/poly''. * Theorems showing that ``distinguishing complexity'' is closely connected to both FewEXP and to EXP. * Hardness results for the problems of approximating formula size and branching program size.
