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Some observations on the probabilistic algorithms and NP-hard problems. (English) Zbl 0483.68045


MSC:

68Q25 Analysis of algorithms and problem complexity
68W99 Algorithms in computer science
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
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References:

[1] Adleman, L.; Manders, K., Reducibility, randomness, and intractability, Ninth Annual ACM Symposium on Theory of Computing, 151-153 (1977)
[2] Bennett, C. H.; Gill, J., Relative to a random oracle A, \(P^A\) ≠ \(NP^A\) ≠ co-\(NP^A\) with probability 1, SIAM J. Comput., 10, 96-113 (1981) · Zbl 0454.68030
[3] Gill, J., Computational complexity of probabilistic Turing machines, SIAM J. Comput., 6, 4, 675-695 (1977) · Zbl 0366.02024
[4] Karp, R. M., Reducibilities among combinatorial problems, (Miller, R. E.; Thatcher, J. W., Complexity of Computer Computations (1972), Plenum Press: Plenum Press New York), 85-104
[5] Karp, R.; Lipton, R., Some connections between nonuniform and uniform complexity classes, Twelfth ACM Symposium on Theory of Computing, 302-309 (1980)
[6] Miller, G. L., Riemann’s hypothesis and tests for primality, J. Comput. System Sci., 13, 300-317 (1976) · Zbl 0349.68025
[7] Pratt, V., Every prime has a succinct certificate, SIAM J. Comput., 4, 214-220 (1975) · Zbl 0316.68031
[8] Rabin, M. O., Probabilistic algorithms, (Traub, J. F., Algorithms and Complexity (1976), Academic Press: Academic Press New York), 21-39 · Zbl 0384.60001
[9] Rackoff, C., Relativized questions involving probabilistic algorithms, Proc. Tenth ACM Symposium on Theory of Computing, 338-342 (1978) · Zbl 1282.68158
[10] Simon, J., On some central problems in computational complexity (1975), Cornell University: Cornell University Ithaca, NY, TR 75-224
[11] Solovay, R.; Strassen, V., A fast Monte-Carlo test for primality, SIAM J. Comput., 84-85 (1977) · Zbl 0345.10002
[12] Stockmeyer, L. J., The polynomial time hierarchy, Theoret. Comput. Sci., 3, 1, 1-22 (1977) · Zbl 0353.02024
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