Bulletin of Symbolic Logic

Von Neumann, Gödel and complexity theory

Alasdair Urquhart

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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.

Article information

Source
Bull. Symbolic Logic Volume 16, Issue 4 (2010), 516-530.

Dates
First available: 4 January 2011

Permanent link to this document
http://projecteuclid.org/euclid.bsl/1294171130

Digital Object Identifier
doi:10.2178/bsl/1294171130

Mathematical Reviews number (MathSciNet)
MR2724531

Citation

Urquhart, Alasdair. Von Neumann, Gödel and complexity theory. Bulletin of Symbolic Logic 16 (2010), no. 4, 516--530. doi:10.2178/bsl/1294171130. http://projecteuclid.org/euclid.bsl/1294171130.


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