Algorithmic randomness and measures of complexity
نویسنده
چکیده
We survey recent advances on the interface between computability theory and algorithmic randomness, with special attention on measures of relative complexity. We focus on (weak) reducibilities that measure (a) the initial segment complexity of reals and (b) the power of reals to compress strings, when they are used as oracles. The results are put into context and several connections are made with various central issues in modern algorithmic randomness and computability.
منابع مشابه
Kolmogorov Complexity and Algorithmic Randomness
This paper aims to provide a minimal introduction to algorithmic randomness. In particular, we cover the equivalent 1-randomness and MartinLöf randomness. After a brief review of relevant concepts in computability, we develop the basic theory of Kolmogorov complexity, including the KC theorem and more general notion of information content measures. We then build two natural definitions of rando...
متن کاملAlgorithmic randomness over general spaces
Algorithmic randomness over general spaces has been considered such as an effective topological space and a computable metric space. In this paper we generalize algorithmic randomness to a computable topological space. First we define computable measures on a computable topological space and study computability of the evaluation. Next we define randomnesses via three approaches. Measure randomn...
متن کاملLecture Notes on Randomness for Continuous Measures
Most studies on algorithmic randomness focus on reals random with respect to the uniform distribution, i.e. the (1/2, 1/2)-Bernoulli measure, which is measure theoretically isomorphic to Lebesgue measure on the unit interval. The theory of uniform randomness, with all its ramifications (e.g. computable or Schnorr randomness) has been well studied over the past decades and has led to an impressi...
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 کاملAlgorithmic complexity for short binary strings applied to psychology: a primer.
As human randomness production has come to be more closely studied and used to assess executive functions (especially inhibition), many normative measures for assessing the degree to which a sequence is randomlike have been suggested. However, each of these measures focuses on one feature of randomness, leading researchers to have to use multiple measures. Although algorithmic complexity has be...
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:
- Bulletin of Symbolic Logic
دوره 19 شماره
صفحات -
تاریخ انتشار 2013