B. Trakhtenbrot. Turing computations with logarithmic delay. Algebra i Logika, 3:33--48, 1964. 37 Home/Search Document Not in Database Summary Related Articles Check |
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A Short History of Computational Complexity - Fortnow, Homer (2002) (Correct)
....for time but also for space and any other measure ful lling a small list of axioms, which we now call Blum complexity measures. Soon after we saw two other major results that we will state for time but also hold for all Blum complexity measures. Independently Borodin [Bor72] and Trakhtenbrot [Tra64] proved the gap theorem: For any computable unbounded r(n) there exist a computable time bound t(n) such that any language computable in time t(n) is also computable in time r(t(n) McCreight and Meyer [MM69] showed the union theorem: Given any computably presentable list of computable time ....
....consequences. It is worth noting that in about the same period there was considerable e ort by Russian mathematicians working on similar combinatorial problems trying to prove that brute force was needed to solve them. Several of these problems eventually turned out to be NP complete as well [Tra64] The existence of NP complete problems was proved independently by Stephen Cook in the United States and Leonid Levin in the Soviet Union. Cook, then a graduate student at Harvard, proved that the satis ability problem is NP complete [Coo71] Levin, a student of Kolmogorov at Moscow State ....
B. Trakhtenbrot. Turing computations with logarithmic delay. Algebra i Logika, 3(4):33-48, 1964.
Levin, Blum and the Time Optimality of Programs - Christensen (1999) (Correct)
....program that solves the problem. We cannot even bound the speedup proved by the theorem: there are problems for which any program that solves the problem is much slower than some other program solving the problem, for any computable definition of much . And unlike the well known Gap Theorem ([11], 3] the result does not rely upon rather unnatural time functions which are not time constructible. Furthermore, a new speedup theorem proved in this thesis also demonstrates that such problems also exist among the feasible ones problems that are computable in polynomial time. Thus, it is ....
B. A. Trakhtenbrot. Turing Computations with Logarithmic Delay. Algebra i Logika, 3(4):33--48, 1964. 73
Reductions in Circuit Complexity: An Isomorphism Theorem.. - Agrawal, Allender, al. (1997) (3 citations) (Correct)
....AC 0 and NC 0 reducibility coincide. This is a gap theorem in the sense that there is a big difference (gap) in the computational power of NC 0 and AC 0 functions, but no difference in their power to perform completeness reductions. This is analogous to the Borodin Trakhtenbrot Gap Theorem [Bo72, Tr64]. Some other similar gap theorems are presented in [Ag94, Ag96] and in [Ag95] it is shown that sometimes, the hypothesis that a gap exists for two reducibilities can have interesting consequences. 5 We do not know if our Isomorphism Theorem holds for Dlogtime uniform AC 0 isomorphisms ....
B. A. Trakhtenbrot, Turing computations with logarithmic delay, Algebra i Logika 3 (1964) 33--48. -- 25 --
Complexity Classes - Allender, Loui, Regan (Correct)
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B. Trakhtenbrot. Turing computations with logarithmic delay. Algebra i Logika, 3:33--48, 1964. 37
Complexity Classes - Allender, Loui, Regan (Correct)
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B. Trakhtenbrot. Turing computations with logarithmic delay. Algebra i Logika, 3:33--48, 1964.
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