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Von Neumann, Gödel and Complexity Theory

Published online by Cambridge University Press:  15 January 2014

Alasdair Urquhart
Alasdair Urquhart*
Affiliation:
Department of Computer Science, 10 King's College Road, University of Toronto, Toronto, Ontario M5S 3G4, Canada. E-mail: urquhart@cs.toronto.edu
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Abstract

Around 1989, a striking letter written in March 1956 from Kurt Gödel to John von Neumann came to light. It poses some problems about the complexity of algorithms; in particular, it asks a question that can be seen as the first formulation of the P = ? NP question. This paper discusses some of the background to this letter, including von Neumann's own ideas on complexity theory. Von Neumann had already raised explicit questions about the complexity of Tarski's decision procedure for elementary algebra and geometry in a letter of 1949 to J. C. C. McKinsey. The paper concludes with a discussion of why theoretical computer science did not emerge as a separate discipline until the 1960s.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 16 , Issue 4 , December 2010 , pp. 516 - 530
Copyright
Copyright © Association for Symbolic Logic 2010

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