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In computational complexity theory, a problem is NP-complete when:
- It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no".
- When the answer is "yes", this can be demonstrated through the existence of a short solution.
- The correctness of each solution can be verified quickly and a brute-force search algorithm can find a solution by trying all possible solutions.
- The problem can be used to simulate every other problem for which we can verify quickly that a solution is correct. In this sense, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. If we could find solutions of some NP-complete problem quickly, we could quickly find the solutions of every other problem to which a given solution can be easily verified.
Richard Ryan Williams, known as Ryan Williams, is an American theoretical computer scientist working in computational complexity theory and algorithms.
In structural complexity theory, the Berman–Hartmanis conjecture is an unsolved conjecture named after Leonard C. Berman and Juris Hartmanis. Informally, it states that all NP-complete languages look alike, in the sense that they can be related to each other by polynomial time isomorphisms.
References
- ↑ "ACM-SIGACT Awards and Prizes: 2007 Gödel Prize".
- ↑ "EATCS: Gödel Prize - 2007". Archived from the original on 2007-12-01.
- ↑ Agrawal, M.; Allender, E.; Rudich, Steven (1998). "Reductions in Circuit Complexity: An Isomorphism Theorem and a Gap Theorem". Journal of Computer and System Sciences. 57 (2). Boston, MA: Academic Press: 127–143. doi: 10.1006/jcss.1998.1583 . ISSN 1090-2724.
- ↑ Oakland.edu
