Computability, Unsolvability, Randomness
by Stephen G. Simpson
Publisher: The Pennsylvania State University 2009
Number of pages: 151
I exposit Turing's 1936 theory of computability and unsolvability, as subsequently developed by Kleene and Post. This theory is of the essence in theoretical computer science and in the study of unsolvable mathematical problems. Second, I provide an introductory account of a research area which is currently very active: algorithmic randomness and Kolmogorov complexity.
Home page url
Download or read it online for free here:
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.
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.
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.
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.