Bulletin of Symbolic Logic

Von Neumann, Gödel and complexity theory

Alasdair Urquhart

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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.

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

First available in Project Euclid: 4 January 2011

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

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