M. Saks. Randomization and derandomization in space-bounded computation. Annual Conference on Structure in Complexity Theory, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....on each step, with the additional property that if x A then at least half of the sequences of nondeterministic choices lead to an accepting state. The class RSPACE(n) is defined analogously. Just as it is conjectured that UL = NL, there is a popular conjecture that RL = L. For example, see [Sak96] This would imply RSPACE(n) DSPACE(n) We also need a logspace analog of the complexity class Few of [CH90] the class LFew (which was called LogFew in [AR98] is the set of all languages A such that there is an NL machine M with the property that for all x, #acc M (x) x , and there is a ....

M. Saks. Randomization and derandomization in space-bounded computation. In Proc. IEEE Conf. on Comput. Complexity, pages 128-- 149, 1996. 15

....of OBDDs is that they model the computation of a randomized space bounded algorithm in a non uniform way. By a space S bounded randomized algorithm, we mean one that uses S bits of workspace, halts in 2 S steps, has an input tape, a random tape and reads every random bit exactly once. See [5] for a survey of the role of randomness to get space ecient algorithms. This connection between OBDDs and randomized space bounded algorithms has been used by Nisan [3] to design a pseudorandom generator to derandomize space bounded randomized algorithms. The design of the pseudorandom generator ....

M. Saks, Randomization and Derandomization in Space-bounded Computation, Computational Complexity, 1996, pp. 128-149.

.... quantum Turing machines We begin by briefly reviewing some relevant facts concerning space bounded quantum computation; for further information see [12] For background on quantum computation more generally, we refer the reader to [3] and [4] and for classical space bounded computation see [11]. The model of computation we use is the quantum Turing machine (QTM) Our QTMs have three tapes: a read only input tape, a work tape, and a write only output tape. The input and work tape alphabets are denoted # and #, respectively, and the output is assumed to be in binary. Since our attention ....

M. Saks. Randomization and derandomization in space-bounded computation. In Proceedings of the 11th Annual IEEE Conference on Computational Complexity, pages 128--149, 1996.

....with the output (x) We can write 0 as a 2 n 2 n matrix with Boolean values, and we say that a Boolean function is in QNC if its reversible version is. We can consider various de nitions of probabilistic acceptance and obtain the classes EQNC, BQNC, and PrQNC in nomenclature drawn from [20, 24]. EQNC accepts exactly, i.e. with probability 1 if the input is in the language and 0 otherwise. BQNC accepts with two sided bounded probability, P 2=3 if the input is in the language and P 1=3 if it is not. PrQNC accepts with probability P 1=2 if the input is in the language and P 1=2 if ....

M. Saks, \Randomization and derandomization in space-bounded computation." Proc. 11th IEEE Conf. on Computational Complexity (1996) 128-149.

....in practice, with the advantage of having a sound motivation for its use. One natural direction for such research would be to seek deterministic extractors for distributions which have spacebounded samplers, rather than time bounded ones as we have. As with pseudorandom generators (cf. Sak96] there is hope for unconditional results in the space bounded setting. The samplers considered by Blum [Blu86] namely finite state Markov chains, can be viewed as a limited form of space bounded of computation, but the extractors given there only work when the number of bits received from the ....

Michael Saks. Randomization and derandomization in space-bounded computation. In Proceedings, Eleventh Annual IEEE Conference on Computational Complexity, pages 128--149, Philadelphia, Pennsylvania, 24--27 May 1996. IEEE Computer Society Press.

.... 2 Space bounded QTMs We begin by briefly discussing some relevant facts concerning space bounded quantum computation; for further information see [14] For background on quantum computation more generally, we refer the reader to [4] and [5] and for classical space bounded computation see [13]. The model of computation we use is the quantum Turing machine (QTM) Our QTMs have two tapes: a read only input tape and a work tape. The input and work tape alphabets are denoted Sigma and Gamma, respectively. The internal states of a QTM are partitioned into two sets: accepting states and ....

M. Saks. Randomization and derandomization in space-bounded computation. In Proceedings of the 11th Annual IEEE Conference on Computational Complexity, pages 128--149, 1996.

....see the survey of Fortnow [10] and the references therein. Counting complexity was applied to space bounded computation in [3, 4] to which the reader is referred to for proofs of the theorems stated in this section. For more general background information on spacebounded computation, see Saks [19]. Consider a nondeterministic Turing machine M running in logspace. On each input x there are some number of computation paths that lead to an accepting configuration and some number of paths that lead to a rejecting configuration; we denote these numbers by #M(x) and #M(x) respectively. ....

M. Saks. Randomization and derandomization in spacebounded computation. In Proceedings of the 11th Annual IEEE Conference on Computational Complexity, pages 128--149, 1996.

....RQSPACE(s) NQSPACE(s) and similarly for the halting almost surely and halting absolutely versions of these classes. The prefixes RQ, BQ, NQ and PrQ may be replaced by R, BP, N and Pr, respectively, to obtain the analogously defined probabilistic classes. Here we have adopted the notation of [20], to which the reader is referred for further information regarding the probabilistic versions of these classes. 3 Classical Simulations of Quantum Machines We consider in this section probabilistic simulations of quantum Turing machine computations. It is proved that probabilistic Turing ....

M. Saks. Randomization and derandomization in space-bounded computation. In Proceedings of the 11th Annual IEEE Conference on Computational Complexity, pages 128--149, 1996.

....Institute of Mathematical Sciences, Chennai 600 113, INDIA. meena imsc.ernet.in Abstract. We clarify the computational complexity of planarity testing, by showing that planarity testing is hard for L, and lies in SL. This nearly settles the question, since it is widely conjectured that L = SL [25]. The upper bound of SL matches the lower bound of L in the context of (nonuniform) circuit complexity, since L poly is equal to SL poly. Similarly, we show that a planar embedding, when one exists, can be found in FL SL . Previously, these problems were known to reside in the complexity ....

....through log 1.5 n [19] to log 4 3 n [3] It is suspected that this trend will continue to eventually reach log n. UGAP can be solved in randomized logspace [1] Recent developments in derandomization techniques have led many researchers to conjecture that randomized logspace is equal to L [25]. In the context of nonuniform complexity theory (for example, as explored in [15, 5] the corresponding nonuniform complexity classes L poly and SL poly are equal. 1 Hence in this setting, the computational complexity of planarity is resolved; it is complete for L poly under projections. One ....

M. Saks. Randomization and derandomization in space-bounded computation. In Proceedings of the 11th Annual Conference on Computational Complexity, pages 128--149. IEEE Computer Society, 1996.

....x with probability less than or equal to 1 2 . If in addition M halts absolutely, then L is in the class XHSPACE(s) The prefixes RQ, BQ, NQ and PrQ may be replaced by R, BP, N and Pr, respectively, to obtain the analogously defined probabilistic classes. Here we have adopted the notation of [23], to which the reader is referred for further information regarding the probabilistic versions of these classes. 3 Relations among quantum classes In this section, we discuss relationships among the space bounded quantum classes defined in the previous section. In the two sections which follow, ....

M. Saks. Randomization and derandomization in space-bounded computation. In Proceedings of the 11th Annual IEEE Conference on Computational

....For polynomial time computation, unfortunately, the currently available constructions of pseudorandom generators 3 all rely on certain unproven assumptions. Nevertheless, for space bounded computation, successful constructions of pseudorandom generators have been obtained. We refer the reader to [Sak96] for a survey on the latter subject. The most often used method in deterministic amplification, on the other hand, is to build a type of bipartite expander called dispersers [Sip88] or its variant called extractors [NZ93] The application of this approach gives extremely high success probability ....

....In this section we give a review of the connection between these two problems and summarize the consequences of our new result. For a general retrospective on the problems and developments in the related subjects of randomized space computation, we refer the reader to the survey by Saks [Sak96]. 10 A randomized space S(n) machine is a nondeterministic Turing machine that runs in space S(n) on any input of length n, and has two nondeterministic choices at any stage of the computation depending on an unbiased coin flip. By standardizing the model, we may assume that the machine has a ....

M. Saks. Randomization and Derandomization in Space-Bounded Computation. In Proc. of 11th Annual Conference on Computational Complexity, 1996.

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M. Saks. Randomization and derandomization in space-bounded computation. Annual Conference on Structure in Complexity Theory, 1996.

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M. Saks. Randomization and derandomization in space-bounded computation. In Proc. IEEE Conf. on Comput. Complexity, pages 128--149, 1996.

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Michael Saks. Randomization and derandomization in space-bounded computation. In Proceedings of the 11th Annual Conference on Computational Complexity, pages 128--149. IEEE Computer Society, 1996.

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M. Saks, \Randomization and derandomization in space-bounded computation." Proc. 11th IEEE Conference on Computational Complexity (1996) 128-149.

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