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 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 Frank Stephan - National University of Singapore
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.
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.
This book is intended as an introductory textbook in Computability Theory and Complexity Theory, with an emphasis on Formal Languages. Its target audience is CS and Math students with some background in programming and data structures.