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Journals and Conferences
We present an unconditional deterministic polynomial-time algorithm that determines whether an input number is prime or composite.
In this paper, we formalize two stepwise approaches, based on pseudo-random generators, for proving P = NP and its arithmetic analog: Permanent requires superpolynomial sized arithmetic circuits.
We show that proving exponential lower bounds on depth four arithmetic circuits imply exponential lower bounds for unrestricted depth arithmetic circuits. In other words, for exponential sized circuits additional depth beyond four does not help. We then show that a complete black-box derandomization of identity testing problem for depth four circuits with… (More)
We give a simple and new randomized primality testing algorithm by reducing primality testing for number <i>n</i> to testing if a specific univariate identity over <i>Z<sub>n</sub></i> holds.We also give new randomized algorithms for testing if a multivariate polynomial, over a finite field or over rationals, is identically zero. The first of these… (More)
A finite state Markov chain M is often viewed as a probabilistic transition system. An alternative view - which we follow here - is to regard M as a linear transform operating on the space of probability distributions over its set of nodes. The novel idea here is to discretize the probability value space [0,1] into a finite set of intervals. A concrete… (More)
Continuing a line of investigation that has studied the function classes #P Val79b], #SAC 1 Val79a, Vin91, AJMV], #L AJ93b, Vin91, AO94], and #NC 1 CMTV96], we study the class of functions #AC 0. One way to deene #AC 0 is as the class of functions computed by constant-depth polynomial-size arithmetic circuits of unbounded fan-in addition and multiplication… (More)
We show that all sets that are c omplete for NP under non-uniform AC 0 reductions are isomorphic under non-uniform AC 0-computable isomorphisms. Furthermore, these sets remain NP-complete even under non-uniform NC 0 reductions. More generally, we show two theorems that hold for any complexity class C closed under uniform NC 1-computable many-one reductions.… (More)