Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A Survey of Some Recent Results on Computational Complexity in Weak Theories of Arithmetic
Proceedings on Mathematical Foundations of Computer Science
The consistency of "P = NP" and related problems with fragments of number theory
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Languages which capture complexity classes
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Number-theoretic aspects of computational complexity.
Number-theoretic aspects of computational complexity.
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
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A semantic, or model theoretic, approach is proposed to study the problems P =? NP and NP =? co-NP. This approach seems to avoid the difficulties that recursion-theoretic approaches appear to face in view of the result of Baker et al. on relativizations of the P =? NP question; moreover, semantical methods are often simpler and more powerful than syntactical ones. The connection between the existence of certain partial extensions of nonstandard models of arithmetic and the question NP =? co-NP is discussed. Several problems are stated about nonstandard models, and a possible link between the Davis-Matijasevi@@@@-Putnam-Robinson theorem on Diophantine sets and the NP =? co-NP question is mentioned.