The consistency of "P = NP" and related problems with fragments of number theory

Authors:
Richard A. DeMillo;Richard J. Lipton
Affiliations:
School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia;Dept. Electrical Engineering & Computer Science, University of California, Berkeley, Berkeley, California
Venue:
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Year:
1980

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Abstract

The main results of this paper demonstrate the consistency of “P &equil; NP” and a variant of “NP @@@@ coNP” with certain natural fragments of number theory to be defined precisely in the sequel.@@@@ Consistency results represent an approach to the lower bound problems of complexity theory which points to a number of interesting lines of inquiry. Our ultimate goal is to make precise the difficulty of proving certain nontrivial lower bounds. Among the possibilities which follow from this approach are: (1) that logical techniques may help us resolve the P &equil; NP question, (2) that showing why certain arguments must fail may lead to mathematical tools capable of resolving the problems, and (3) that the special character of model theoretic methods in complexity theory may lead to new results which are of purely logical interest. We will address these possibilities below.