W. Lindner. On the polynomial time bounded measure of one-truthtable degrees and p-selectivity, 1993. Diplomarbeit, Technische Universit at Berlin.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....We have two reasons for interest in this question. First and foremost, many recent investigations in complexity theory focus on the resource bounded measure of the upper P r span P Gamma1 r (A) fBjA P r Bg of a language A. Such investigations include work on small span theorems [9, 14, 4, 11, 7] and work on the BPP versus E question [1, 7, 8] In general, the upper P r span of a language is closed upwards, but not downwards, under P r reductions. Our second reason for interest in upward closure conditions is that the above mentioned results of Breutzmann and Lutz [5] do not fully ....

....for SST ( P r ; E) Similar assertions for other classes, e.g. SST ( P r ; E 2 ) are defined in the now obvious manner. Juedes and Lutz [9] proved the first small span theorems, SST( P m ; E) and SST( P m ;E 2 ) and noted that extending either to P T would establish E 6 BPP. Lindner [14] established SST( P 1 Gammatt ; E) and SST( P 1 Gammatt ; E 2 ) and Ambos Spies, Neis, and Terwijn [4] proved SST( P k Gammatt ; E) and SST( P k Gammatt ; E 2 ) for all fixed k 2 N. Very recently, Buhrman and van Melkebeek [7] have taken a major step forward by proving SST( P ....

W. Lindner. On the polynomial time bounded measure of one-truth-table degrees and p-selectivity, 1993. Diplomarbeit, Technische Universitat Berlin.

....of pseudorandom generators and one way functions with exponential nonuniform security. It is thus to be hoped that a systematic investigation of Small Span Theorems will shed useful light on such fundamental questions. Some initial steps in this investigation have already been taken. Lindner [34] adapted the method of [26] to prove Small Span Theorems for P 1 Gammatt reductions in E and E 2 . Ambos Spies, Neis, and Terwijn [5] used resource bounded genericity to generalize the method of [26] thereby obtaining Small Span Theorems for P k Gammatt reductions in E and E 2 for all ....

W. Lindner, On the polynomial time bounded measure of one-truth-table degrees and pselectivity, Diplomarbeit, Technische Universitat Berlin, 1993.

....Neis, and Terwijn [6] used this method to prove a new result on resource bounded measure, namely, the Small Span Theorem for P k Gammatt reductions. This extended the Small Span Theorems for P m reductions and P 1 Gammatt reductions proven by Juedes and Lutz [11] and Lindner [12], respectively. Ambos Spies, Neis, and Terwijn [4] Ambos Spies [1] and Ambos Spies and Mayordomo [4] have also used this method to reprove a number of previously known results on resource bounded measure. To date, every such genericity proof of a resource bounded measure result corresponds ....

W. Lindner. On the polynomial time bounded measure of one-truth-table degrees and p-selectivity, 1993. Diplomarbeit, Technische Universitat Berlin.

....new insights concerning completeness phenomena. Such insights include the existence and distribution of weakly complete problems [12, 7, 3, 10] lower bounds on the density and complexity of weakly complete problems [15, 9, 8] upper bounds on the complexity and abundance of complete problems [9, 11, 2, 8, 17], and various consequences of the hypothesis that SAT is weakly complete for exponential time [16, 9, 15, 14] A recurring tool and unifying theme of much of this work is the development of Small Span Theorems for various reducibilities and complexity classes. Briefly, given a reducibility R and ....

....of pseudorandom generators and one way functions with exponential nonuniform security. It is thus to be hoped that a systematic investigation of Small Span Theorems will shed useful light on such fundamental questions. Some initial steps in this investigation have already been taken. Lindner [11] adapted the method of [9] to prove Small Span Theorems for P 1 Gammatt reductions in E and E 2 . AmbosSpies, Neis, and Terwijn [2] used resource bounded genericity to generalize the method of [9] thereby obtaining Small Span Theorems for P k Gammatt reductions in E and E 2 for all ....

W. Lindner, On the polynomial time bounded measure of one-truth-table degrees and p-selectivity, Diplomarbeit, Technische Universitat Berlin, 1993.

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W. Lindner. On the polynomial time bounded measure of one-truthtable degrees and p-selectivity, 1993. Diplomarbeit, Technische Universit at Berlin.

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