The complexity of theorem-proving procedures

@article{Cook1971TheCO,
  title={The complexity of theorem-proving procedures},
  author={Stephen A. Cook},
  journal={Proceedings of the third annual ACM symposium on Theory of computing},
  year={1971}
}
  • S. Cook
  • Published 3 May 1971
  • Mathematics, Computer Science
  • Proceedings of the third annual ACM symposium on Theory of computing
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… 
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