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Sparse complete sets for NP: solution of a conjecture of Berman and Hartmanis. (English) Zbl 0493.68043

##### MSC:
 68Q25 Analysis of algorithms and problem complexity 03D15 Complexity of computation (including implicit computational complexity) 03D30 Other degrees and reducibilities in computability and recursion theory
##### Keywords:
NP-complete sets; polynomial-time hierarchy
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##### References:
 [1] Aho, A.; Hopcroft, J.; Ullman, J., The design and analysis of computer algorithms, (1974), Addison-Wesley Reading, Mass [2] Berman, L.; Hartmanis, J.; Berman, L.; Hartmanis, J., On isomorphisms and density of NP and other complete sets, (), 6, 30-40, (1977) · Zbl 0356.68059 [3] Berman, P., Relationship between density and deterministic complexity of NP-complete languages, (), 63-71 [4] Book, R.; Wrathall, C.; Selman, A.; Dobkin, D., Inclusion complete tally languages and the hartmanis-berman conjecture, Math. systems theory, 11 (, 1-8, (1977) · Zbl 0365.68044 [5] Cook, S., The complexity of theorem proving procedures, (), 151-158 [6] Fortune, S., A note on sparse complete sets, SIAM. J. comput., 8, 431-433, (1979) · Zbl 0415.68006 [7] Gill, J., Computational complexity of probabilistic Turing machines, SIAM J. comput., 6, 675-695, (1977) · Zbl 0366.02024 [8] Hartmanis, J.; Mahaney, S., On census complexity and sparseness of NP-complete sets, Cornell university, computer science department technical report TR 80-416, Ithaca. New York, (April 1980) [9] Hartmanis, J.; Mahaney, S.; Hartmanis, J.; Mahaney, S., An essay about research on sparse NP-complete sets, (), Cornell university, department of computer science technical report TR 80-244, (1980) · Zbl 0444.68032 [10] Hopcroft, J.; Ullman, J., Introduction to automata theory, languages, and computation, (1979), Addison-Wesley Reading, Mass · Zbl 0426.68001 [11] Karp, R., Reducibility among combinatorial problems, (), 85-103 · Zbl 0366.68041 [12] Karp, R.; Lipton, R., Some connections between nonuniform and uniform complexity classes, (), 302-309 [13] \scT. Long, “A Note on Cosparse Polynomial Time Turing Complete Sets for NP,” to appear. [14] Mahaney, S., Sparse NP-complete sets, () · Zbl 0444.68032 [15] Meyer, A.; Paterson, M., With what frequency are apparently intractable problems difficult?, MIT technical report, (February 1979) [16] Meyer, A.; Stockmeyer, L., The equivalence problem for regular expressions with squaring requires exponential time, (), 125-129 [17] Simon, J., On the difference between one and many, (), 480-491 [18] \scJ. Simon and S. Mahaney, to appear. [19] Stockmeyer, L., The polynomial time hierarchy, Theoret. comput. sci., 3, 1-22, (1976) · Zbl 0353.02024 [20] Valiant, L., On the complexity of computing the permanent, Theoret. comput. sci., 8, 189-202, (1979) · Zbl 0415.68008
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