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The complexity of theorem-proving procedures (1971)
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| Venue: | IN STOC |
| Citations: | 1049 - 5 self |
BibTeX
@INPROCEEDINGS{Cook71thecomplexity,
author = {Stephen A. Cook},
title = {The complexity of theorem-proving procedures},
booktitle = {IN STOC},
year = {1971},
pages = {151--158},
publisher = {ACM}
}
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Abstract
It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology. Here “reduced ” means, roughly speaking, that the first problem can be solved deterministically in polynomial time provided an oracle is available for solving the second. From this notion of reducible, polynomial degrees of difficulty are defined, and it is shown that the problem of determining tautologyhood has the same polynomial degree as the problem of determining whether the first of two given graphs is isomorphic to a subgraph of the second. Other examples are discussed. A method of measuring the complexity of proof procedures for the predicate calculus is introduced and discussed. Throughout this paper, a set of strings 1 means a set of strings on some fixed, large, finite alphabet Σ. This alphabet is large enough to include symbols for all sets described here. All Turing machines are deterministic recognition devices, unless the contrary is explicitly stated.
Keyphrases
theorem-proving procedure polynomial degree many proposition symbol binary notation polynomial re-reducibility predicate calculus polynomial time propositional formula finite alphabet turing machine propositional calculus first problem proof procedure deterministic recognition device polynomial time-bounded nondeterministic turing machine recognition problem
