Complexity and Randomness
نویسندگان
چکیده
2 Random finite strings 7 2.1 Plain Kolmogorov complexity . . . . . . . . . . . . . . . . . . 7 2.2 Prefix-free complexity . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Kraft inequality, Shannon-Fano code . . . . . . . . . . . . . . 9 2.4 The universal semimeasure m . . . . . . . . . . . . . . . . . . 10 2.5 A priori probability . . . . . . . . . . . . . . . . . . . . . . . . 11 2.6 Coding, symmetry, and counting . . . . . . . . . . . . . . . . 12
منابع مشابه
Chaos/Complexity Theory and Education
Sciences exist to demonstrate the fundamental order underlying nature. Chaos/complexity theory is a novel and amazing field of scientific inquiry. Notions of our everyday experiences are somehow in connection to the laws of nature through chaos/complexity theory’s concerns with the relationships between simplicity and complexity, between orderliness and randomness (Retrieved from http://www.inc...
متن کاملAnother Motivation for Reducing the Randomness Complexity of Algorithms
We observe that the randomness-complexity of an algorithm effects the time-complexity of implementing a version of it that utilizes a weak source of randomness (through a randomness-extractor). This provides an additional motivation for the study of the randomness complexity of randomized algorithms. We note that this motivation applies especially in the case that derandomization is prohibiting...
متن کاملIs Randomness native to Computer Science? Ten Years Later
2 What we have learned? A personal pick 4 2.1 From randomness to complexity . . . . . . . . . . . . . . . . . . . . . 4 2.2 Formalization of randomness: infinite strings . . . . . . . . . . . . . 5 2.3 Random versus lawless . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Randomness and finite strings: incompressibility . . . . . . . . . . . 7 2.5 Representation and Kolmogorov complexi...
متن کاملAlgorithmic Information Theory and Kolmogorov Complexity
This document contains lecture notes of an introductory course on Kolmogorov complexity. They cover basic notions of algorithmic information theory: Kolmogorov complexity (plain, conditional, prefix), notion of randomness (Martin-Löf randomness, Mises–Church randomness), Solomonoff universal a priori probability and their properties (symmetry of information, connection between a priori probabil...
متن کاملReducing the Randomness Complexity of Property Testing, with an Emphasis on Testing Bipartiteness
Property testers are algorithms whose goal is distinguishing between inputs that have a certain property and inputs which are far from all instances with this property. We show that for a wide variety of properties, there exists no deterministic tester that queries only a sublinear number of input entries. Therefore, most sublinear property testers must be probabilistic algorithms. Nevertheless...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003