D. Sivakumar. Probabilistic Techniques in Structural Complexity Theory. PhD thesis, SUNY Buffalo, 1996.  Home/Search   Document Details and Download   Summary   Related Articles

....extend in any obvious way to classes smaller than P. Nonetheless, a notion of measure on P that generalizes Lutz s notion was defined in [AS94] thus successfully overcoming this first obstacle. Using many techniques developed for proving lower bounds for AC 0 , Cai, Sivakumar, and Strauss [CSS, Siv96] succeeded in showing that not only is NTIME(logn) a measure zero subset of P, but in fact all of AC 0 has measure zero in P (using a notion of measure that differs only slightly from that of [AS94] This is the most exciting application of resource bounded measure on P thus far, and it also ....

.... application of resource bounded measure on P thus far, and it also gives cause to reconsider how likely it is that NP is a measure zero subset of DTIME(2 n O(1) There are also results (using a slightly different notion of measure) showing that AC 0 (2) does not have P measure zero [Siv96] Since the Nisan Wigderson pseudorandom generator is an important tool in proving the measure zero result of [CSS] it is tempting to speculate that there is a connection between these contrasting measure results for AC 0 and AC 0 (2) and our inability thus far to construct pseudorandom ....

D. Sivakumar. Probabilistic Techniques in Structural Complexity Theory. PhD thesis, SUNY Buffalo, 1996.

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