by Wilfried Sieg
Publisher: Carnegie Mellon University 2006
Number of pages: 125
Computability is the basic theoretical concept for computer science, artificial intelligence and cognitive science. This essay discusses, at its heart, methodological issues that are central to any mathematical theory that is to reflect parts of our physical or intellectual experience.
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by Andre Nies - Oxford University Press
Covering the basics as well as recent research results, this book provides an introduction to the interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.
by Dag Normann - The University of Oslo
This text is consisting of two parts, Classical Computability Theory and Generalized Computability Theory. We assume that the reader is familiar with the standard vocabulary of logic and set theory, but no advanced background from logic is required.
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I exposit Turing's theory of computability and unsolvability, as subsequently developed by Kleene and Post. Second, I provide an introductory account of a research area which is currently very active: algorithmic randomness and Kolmogorov complexity.
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Recursion theory deals with the fundamental concepts on what subsets of natural numbers could be defined effectively and how complex the so defined sets are. This text gives an overview on the basic results and proof methods in recursion theory.