Algorithmically random sequence

Known as: Martin-Löf randomness, Algorithmically random, Martin-Loef random

Intuitively, an algorithmically random sequence (or random sequence) is an infinite sequence of binary digits that appears random to any algorithm…

Papers overview

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2016

Abstract In this article, I consider the status of several statements analogous to the Church–Turing thesis that assert that some…

2015

We study algorithmically random closed subsets of $\cs$\!, algorithmically random continuous functions from $\cs$ to $\cs$\!, and…

2013

In this paper, a number of almost-everywhere convergence theorems are looked at using computable analysis and algorithmic…

2010

Kolmogorov complexity is the basis of algorithmic randomness theory. It quantifies the amount of information of individual object…

2009

We define the notion of indifferent set with respect to a given class of {0,1}-sequences. Roughly, for a set A in the class, a…

2008

We propose here an extension of Rice’s Theorem to first-order logic, proven by totally elementary means. If P is any property…

2008

We investigate notions of randomness in the space $${{\mathcal C}(2^{\mathbb N})}$$ of continuous functions on $${2^{\mathbb N…

2006

Is the universe computable? If yes, is it computationally a polynomial place? In standard quantum mechanics, which permits…

1996

Spectral quantities associated to pairs of matrices are hard-when not impossible-to compute and to approximate* Abstract We…

1994

In this paper languages "bounded reducible" to algorithmically random languages are studied; these are the languages whose…