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Checking identities is computationally intractable NP-hard and therefore human provers will always be needed
Article first published online: 12 JAN 2004
DOI: 10.1002/int.10149
Copyright © 2004 Wiley Periodicals, Inc.
Issue
1098-111X/asset/cover.gif?v=1&s=7f7c12f2c86265974044b2b3f9936860ffc468a0 "International Journal of Intelligent Systems")
International Journal of Intelligent Systems
Special Issue: Intelligent Technologies
Volume 19, Issue 1-2, pages 39–49, January - February 2004
Additional Information
How to Cite
Kreinovich, V. and Tao, C.-W. (2004), Checking identities is computationally intractable NP-hard and therefore human provers will always be needed. Int. J. Intell. Syst., 19: 39–49. doi: 10.1002/int.10149
Publication History
- Issue published online: 12 JAN 2004
- Article first published online: 12 JAN 2004
Funded by
- National Science Foundation (NSF). Grant Numbers: CDA-9015006, EEC-9322370, DUE-9750858, CDA-9522207, EAR-0112968, EAR-0225670, 9710940 Mexico/Conacyt
- National Aeronautics and Space Administration (NAS). Grant Numbers: NCC5-209, NCC2-1232
- Future Aerospace Science and Technology Program (FAST) Center for Structural Integrity of Aerospace Systems
- Air Force Office of Scientific Research
- Air Force Materiel Command
- U.S. Air Force (USAF). Grant Numbers: F49620-95-1-0518, F49620-00-1-0365
- Abstract
- References
- Cited By
Abstract
A 1990 article in the American Mathematical Monthly has shown that most combinatorial identities of the type described in Monthly problems can be solved by known identity checking algorithms. A natural question arises: are these algorithms always feasible or can the number of computational steps be so big that application of these algorithms sometimes is not physically feasible? We prove that the problem of checking identities is nondeterministic polynomial (NP) hard, and thus (unless NP = P) for every algorithm that solves it, there are cases in which this algorithm would require exponentially long running time and thus will not be feasible. This means that no matter how successful computers are in checking identities, human mathematicians will always be needed to check some of them. © 2004 Wiley Periodicals, Inc.