Universal recursively enumerable sets of strings
Reads0
Chats0
TLDR
The main topics of the present work are universal machines for plain and prefix-free description complexity and their domains and the question whether every domain of a universal plain machine is the superset of the domain of some universal prefix- free machine is discussed.About:
This article is published in Theoretical Computer Science.The article was published on 2011-05-01 and is currently open access. It has received 14 citations till now. The article focuses on the topics: Recursively enumerable language & Turing machine.read more
Citations
More filters
Journal ArticleDOI
Generic algorithms for halting problem and optimal machines revisited
TL;DR: It is shown that the fraction of terminating programs cannot have a limit, and all limit points are Martin-L\"of random reals", which means that the halting problem cannot be solved for "most" inputs.
Posted ContentDOI
Universality and Almost Decidability
TL;DR: It is proved the existence of infinitely many universal functions whose halting sets are generic (negligible, i.e. have density zero) and (not) almost decidable.
Journal ArticleDOI
Universality and Almost Decidability
TL;DR: It is proved the existence of infinitely many universal functions whose halting sets are generic negligible, i.e. have density zero and not almost decidable andolves an open problem in [9].
Posted Content
Aspects of Chaitin's Omega.
TL;DR: The purpose of this survey is to expose developments and tell a story about Omega, which outlines its multifaceted mathematical properties and roles in algorithmic randomness.
Book ChapterDOI
What Percentage of Programs Halt
TL;DR: It is shown that the ratio of the number of halting programs of length at most n by the total number of such programs does not have a limit value, and the reals which can be the limsup of such a sequence are further characterised.
References
More filters
Book
An Introduction to Kolmogorov Complexity and Its Applications
Ming Li,Paul M. B. Vitányi +1 more
TL;DR: The Journal of Symbolic Logic as discussed by the authors presents a thorough treatment of the subject with a wide range of illustrative applications such as the randomness of finite objects or infinite sequences, Martin-Loef tests for randomness, information theory, computational learning theory, the complexity of algorithms, and the thermodynamics of computing.
An Introduction to Kolmogorov Complexity and Its Applications
Ming Li,Paul M. B. Vitányi +1 more
TL;DR: The book presents a thorough treatment of the central ideas and their applications of Kolmogorov complexity with a wide range of illustrative applications, and will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics.
Journal ArticleDOI
The definition of random sequences
TL;DR: It is shown that the random elements as defined by Kolmogorov possess all conceivable statistical properties of randomness and can equivalently be considered as the elements which withstand a certain universal stochasticity test.
Book
Classical recursion theory
TL;DR: Theories of Recursive functions, Hierarchies of recursive functions, and Arithmetical sets: Recursively enumerable sets.
Book
Algorithmic Information Theory
TL;DR: This paper reviews algorithmic information theory, which is an attempt to apply information-theoretic and probabilistic ideas to recursive function theory.