Add to ORKGWe study the notion of universality probability of a universal prefix-free machine, as introduced by C. S. Wallace. We show that it is random relative to the third iterate of the halting problem and determine its Turing degree and its place in the arithmetical hierarchy of complexity. Furthermore, we give a computational characterization of the real numbers that are universality probabilities of universal prefix-free machines
Abstract. We prove a number of results in effective randomness, using methods in which Π01 classes p...
AbstractThere are two fundamental computably enumerable sets associated with any Kolmogorov complexi...
We prove that any Chaitin Ω number (i.e., the halting probability of a universal self-delimiting Tur...
We introduce the {it natural halting probability} and the {it natural complexity} of a Turing ma...
AbstractUniversality, provability and simplicity are key notions in computability theory. There are ...
This thesis examines some problems related to Chaitin’s Ω number. In the first section, we describe ...
AbstractIn this paper we introduce the notion of ε-universal prefix-free Turing machine (ε is a comp...
AbstractThe present work investigates several questions from a recent survey of Miller and Nies rela...
Abstract. As a natural example of a 1-random real, Chaitin proposed the halting probability Ω of a u...
The present work investigates several questions from a recent survey of Miller and Nies related to C...
The halting probability of a Turing machine is the probability that the machine will halt if it star...
A Chaitin Omega number is the halting probability of a universal prefix-free Turing machine. Every O...
AbstractLet UTM(m, n) be the class of universal Turing machine with m states and n symbols. Universa...
AbstractWe give a general theorem that provides examples of n-random reals à la Chaitin, for every n...
A real is computable if it is the limit of a computable, increasing, computably converging sequence ...
Abstract. We prove a number of results in effective randomness, using methods in which Π01 classes p...
AbstractThere are two fundamental computably enumerable sets associated with any Kolmogorov complexi...
We prove that any Chaitin Ω number (i.e., the halting probability of a universal self-delimiting Tur...
We introduce the {it natural halting probability} and the {it natural complexity} of a Turing ma...
AbstractUniversality, provability and simplicity are key notions in computability theory. There are ...
This thesis examines some problems related to Chaitin’s Ω number. In the first section, we describe ...
AbstractIn this paper we introduce the notion of ε-universal prefix-free Turing machine (ε is a comp...
AbstractThe present work investigates several questions from a recent survey of Miller and Nies rela...
Abstract. As a natural example of a 1-random real, Chaitin proposed the halting probability Ω of a u...
The present work investigates several questions from a recent survey of Miller and Nies related to C...
The halting probability of a Turing machine is the probability that the machine will halt if it star...
A Chaitin Omega number is the halting probability of a universal prefix-free Turing machine. Every O...
AbstractLet UTM(m, n) be the class of universal Turing machine with m states and n symbols. Universa...
AbstractWe give a general theorem that provides examples of n-random reals à la Chaitin, for every n...
A real is computable if it is the limit of a computable, increasing, computably converging sequence ...
Abstract. We prove a number of results in effective randomness, using methods in which Π01 classes p...
AbstractThere are two fundamental computably enumerable sets associated with any Kolmogorov complexi...
We prove that any Chaitin Ω number (i.e., the halting probability of a universal self-delimiting Tur...