U. V. Vazirani and V. V. Vazirani, Random polynomial time is equal to semi-random polynomial time, Proc. 26th Annual IEEE Symposium on Foundations of Computer Science (1985) 417 - 428.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....possible connections with control theory are pointed out. Some typical results are: It is impossible to improve the quality of individual bits [SV] sampled from such an adversary source. On the other hand the amount of randomness inherent in the source suffices for running randomized algorithms [VV]. A survey of this area may be found in [BLS] The most recent progress in the area of amplifying randomness can be found in [Zu] and the references therein. 5.6 Amortized Cost and the Quality of On Line Decisions A common problem which arises in many situations in economics is that decisions ....

U. V. Vazirani and V. V. Vazirani, Random polynomial time is equal to semi-random polynomial time, Proc. 26th Annual IEEE Symposium on Foundations of Computer Science (1985) 417 - 428.

....impossible to extract even a single almost random bit from one such source (so Vazirani [Va2, Va3] showed how to extract almost random bits from two independent sources) In light of this result, one might give up hope for simulating randomized algorithms with one semi random source. Nevertheless, [VV] and [Va1] showed how to simulate RP and BPP with one semi random source. Chor and Goldreich [CG1] generalized this model by assuming no sequence of l bits has too high a probability of being output. More precisely, 1 Definition 2 [CG1] An (l; ffi) PRB source outputs R bits as R=l blocks Y 1 ; ....

....all of this previous work, it is natural to ask: what is the most general model of a weak source for which we can simulate randomized algorithms Do we need the randomness in some particular form, or will any form suffice Of course, if BPP = P, then we don t need randomness at all. Yet we follow [VV], Va1] and [CG1] and deal with a more abstract BPP problem: let an adversary label strings in f0; 1g r either yes or no, provided that at least 3=4 of the strings have the same label. We wish to find out whether the majority say yes or no, with high probability. It is clear that ....

U. Vazirani and V. Vazirani, "Random Polynomial Time is Equal to Semi-Random Polynomial Time," 26th Annual Symposium on Foundations of Computer Science, 1985, pp. 417-428.

.... with a relatively small extra cost of random bits [KPS85, CG86] The problems of extracting fully random bits from the outputs of imperfect random sources and simulating probabilistic algorithms with such outputs have been studied for a variety of imperfect random sources [VN51, Blu84, SV84, VV85, Vaz86, CG85, CGH 85, BOL85, KKL88, LLS87] Bit extraction has been proved possible in some cases [VN51, Blu84, CGH 85] yielding immediately simulations of probabilistic algorithms with these sources. In other cases bit extraction was proved to be impossible [SV84, CG85, CGH 85, ....

.... 85] yielding immediately simulations of probabilistic algorithms with these sources. In other cases bit extraction was proved to be impossible [SV84, CG85, CGH 85, BOL85, KKL88, LLS87] Simulations of probabilistic algorithms when bit extraction is impossible, have been given in some cases [VV85, Vaz86, CG85] 1.2 The Approach of This Paper. The approach of this paper is to translate the simulation of probabilistic algorithms to the following statistical problem: Given a finite domain X estimate with high confidence the size of a sufficiently large subset S ae X , using a small number ....

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U. V. Vazirani and V. V. Vazirani. Random polynomial time is equal to semi random polynomial time. In FOCS, pages 417--428, 1985.

.... these notes is due to Impagliazzo and Zuckerman [17] Our description is based on expositions in Wigderson s notes [38] and Schoning s book [31] Using expander graphs a similar result is proved in [11] The problem of simulating BPP algorithms with weak random sources was initiated and studied in [28, 35, 36]. More recently, the results of these papers have been substantially improved in [39, 34] 4 Randomization and Interaction Recall that the polynomial hierarchy is built up by setting up a Prover Challenger game, with a polynomial time verifier acting as referee. There is another way in which NP ....

U. Vazirani, V. Vazirani. Random polynomial time is equal to semirandom polynomial time. 26th Annual Symposium on Foundations of Computer Science, 417--428, 1985.

....since they allow transition probabilities to be real numbers. However, there is extensive work showing that probabilistic computation can be carried out in a such a way that it is so insensitive to the transition probabilities that they can be allowed to vary arbitrarily in a large range [34, 44, 47]. In this paper, we show in a similar sense, that quantum Turing Machines are discrete devices: the transition amplitudes need only be accurate to O(log T ) bits of precision to support T steps of computation. As Lipton [30] pointed out, it is crucial that the number of bits is O(log T ) and not ....

Vazirani, U. and Vazirani, V., Random polynomial time is equal to semi-random polynomial time, Proceedings of the 26th Annual IEEE Symposium on Foundations of Computer Science, 1985.

....since they allow transition probabilities to be real numbers. However, there is extensive work showing that probabilistic computation can be carried out in a such a way that it is so insensitive to the transition probabilities that they can be allowed to vary arbitrarily in a large range [34, 44, 47]. In this paper, we show in a similar sense that QTMs are discrete devices: the transition amplitudes need only be accurate to O(log T ) bits of precision to support T steps of computation. As Lipton [30] pointed out, it is crucial that the number of bits is O(log T ) and not O(T ) as it was in ....

<F4.08e+05> U. Vazirani and V.<F4.039e+05> Vazirani,<F4.112e+05> Random polynomial time is equal to semi-random polynomial<F4.039e+05> time, in Proc. 26th Annual IEEE Symposium on Foundations of Computer Science, 1985, pp. 417--428.

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