Introduction to Computability Theory
by Dag Normann
Publisher: The University of Oslo 2010
Number of pages: 95
This text is essentially consisting of two parts, Classical Computability Theory and Generalized Computability Theory. We will 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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by Stephen G. Simpson - The Pennsylvania State University
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.
by Wilfried Sieg - Carnegie Mellon University
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 theory that is to reflect parts of our experience.
by Neil D. Jones - The MIT Press
The author builds a bridge between computability and complexity theory and other areas of computer science. Jones uses concepts familiar from programming languages to make computability and complexity more accessible to computer scientists.
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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.