Von Neumann, Gödel and complexity theory

Bulletin of Symbolic Logic 16 (4):516-530 (2010)
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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

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Alasdair Urquhart
University of Toronto, St. George Campus

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References found in this work

On Axiomatizability Within a System.William Craig - 1953 - Journal of Symbolic Logic 18 (1):30-32.
A Decision Method for Elementary Algebra and Geometry.Alfred Tarski - 1949 - Journal of Symbolic Logic 14 (3):188-188.
A Decision Method for Elementary Algebra and Geometry.Alfred Tarski - 1952 - Journal of Symbolic Logic 17 (3):207-207.
Alfred Tarski, Life and Logic.Anita Burdman Feferman & Solomon Feferman - 2005 - Bulletin of Symbolic Logic 11 (4):535-540.

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