[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference

30 June-3 July 1991

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Displaying Results 1 - 25 of 39
  • Counting classes are at least as hard as the polynomial-time hierarchy

    Publication Year: 1991, Page(s):2 - 12
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (763 KB)

    It is shown that many natural counting classes are at least as computationally hard as PH (the polynomial-time hierarchy) in the following sense: for each K of the counting classes, every set in K(PH) is polynomial-time randomized many-one reducible to a set in K with two-sided exponentially small error probability. As a consequence, these counting classes are computationally harder than PH unless... View full abstract»

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  • PP is closed under truth-table reductions

    Publication Year: 1991, Page(s):13 - 15
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (149 KB)

    R. Beigel et al. (1991) showed that PP is closed under intersection and a variety of special cases of truth-table closure. In the present work, the authors extend the techniques of Beigel et al. to show that PP is closed under general polynomial-time truth-time reductions.<<ETX>> View full abstract»

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  • A complexity theory for feasible closure properties

    Publication Year: 1991, Page(s):16 - 29
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (991 KB)

    The authors propose and develop a complexity theory of feasible closure properties. For each of the classes Hash P, SpanP, OptP, and MidP, they establish complete characterizations-in terms of complexity class collapses-of the conditions under which the class has all feasible closure properties. In particular, Hash P is P-closed if and only if PP=UP; SpanP is P-closed if and only if R-MidP is P-cl... View full abstract»

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  • Gap-definable counting classes

    Publication Year: 1991, Page(s):30 - 42
    Cited by:  Papers (18)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (752 KB)

    The function class Hash P lacks a crucial closure property: it is not closed under subtraction. To remedy this problem, the authors introduce the function class GapP as a natural alternative to Hash P. GapP is the closure of Hash P under subtraction, and has all the other useful closure properties of Hash P as well. It is shown that most previously studied counting classes are gap-definable, i.e.,... View full abstract»

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  • The power of witness reduction

    Publication Year: 1991, Page(s):43 - 59
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1004 KB)

    Recent results by M. Ogiwara and L.A. Hemachandra (1990) established a connection between functions being hard for a class of functions and functions interacting with the class to effect witness reduction. The author believes that the ability to achieve some form of witness reduction is what makes a function hard for a class of functions. To support this thesis he defines new function classes and ... View full abstract»

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  • Proceedings of the Sixth Annual Structure in Complexity Theory Conference (Cat. No.91CH3022-1)

    Publication Year: 1991
    Request permission for commercial reuse | PDF file iconPDF (689 KB)
    Freely Available from IEEE
  • Bounded queries in recursion theory: a survey

    Publication Year: 1991, Page(s):62 - 78
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (858 KB)

    The author surveys much of the work that has been done on the following two questions: (1) What functions can one compute with m queries to A? and (2) Are there functions that can be computed with m queries to A that cannot be computed with m-1 queries to A? To any set X? The framework is recursion-theoretic; the computations have no time or space bound.<<ETX>> View full abstract»

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  • On reductions of NP sets to sparse sets

    Publication Year: 1991, Page(s):79 - 88
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (517 KB)

    M. Ogiwara and O. Watanabe (1990) showed that if SAT is bounded truth-table reducible to a sparse set, then P=NP. In the present work, the authors simplify their proof, strengthen the result, and use it to obtain several new results. Among the new results are the following: applications of the main theorem to log-truth-table and log-Turing reductions of NP sets to sparse sets; generalizations of t... View full abstract»

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  • On the computational complexity of small descriptions

    Publication Year: 1991, Page(s):89 - 101
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (895 KB)

    For a set L that is polynomial time reducible to some sparse set, the authors investigate the computational complexity of such sparse sets relative to L. They construct sets A and B such that both of them are polynomial time reducible to some sparse set, but A (resp., B) is polynomial time reducible to no sparse set in P/sup A/ (resp., NP/sup B/ intersection co-NP/sup B/); that is, the complexity ... View full abstract»

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  • Complexity classes and sparse oracles

    Publication Year: 1991, Page(s):102 - 108
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (395 KB)

    The authors obtain positive relativization results. In particular, the goal is to prove statements of the kind: 'Given two complexity classes C/sub 1/ and C/sub 2/, C/sub 1/=C/sub 2/ if and only if for every sparse set S, C/sub 1//sup S/=C/sub 2//sup S/.' The authors derive a sufficient condition to obtain such results and, as an application, they prove a general theorem from which, as far as they... View full abstract»

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  • PSPACE is provable by two provers in one round

    Publication Year: 1991, Page(s):110 - 115
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (374 KB)

    It is shown that every language in PSPACE, or equivalently every language accepted by an unbounded round interactive proof system, has a one-round, two-prover interactive proof with exponentially small error probability. To obtain this result, the correctness of a simple but powerful method for parallelizing two-prover interactive proofs to reduce their error is proved.<<ETX>> View full abstract»

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  • On the success probability of the two provers in one-round proof systems

    Publication Year: 1991, Page(s):116 - 123
    Cited by:  Papers (24)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (562 KB)

    The author addresses the problem of reducing the error probability of two-prover one-round proof systems, without increasing the number of provers or the number of rounds. An example, the noninteractive agreement protocol, where executing such a protocol twice in parallel does not decrease the error probability at all is constructed. Upper bounds on the error probability of specific classes of pro... View full abstract»

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  • On the random-self-reducibility of complete sets

    Publication Year: 1991, Page(s):124 - 132
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (612 KB)

    Informally, a function f is random-self-reducible if the evaluation of f at any given instance x can be reduced in polynomial time to the evaluation of f at one or more random instances y/sub i/. A set is random-self-reducible if its characteristic function is. The authors generalize the previous formal definitions of random-self-reducibility. They show that, even under this very general definitio... View full abstract»

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  • One-way functions, hard on average problems, and statistical zero-knowledge proofs

    Publication Year: 1991, Page(s):133 - 138
    Cited by:  Papers (15)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (425 KB)

    The author studies connections among one-way functions, hard on the average problems, and statistical zero-knowledge proofs. In particular, he shows how these three notions are related and how the third notion can be better characterized, assuming the first one.<<ETX>> View full abstract»

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  • On one query, self-reducible sets

    Publication Year: 1991, Page(s):139 - 151
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (869 KB)

    The authors study one-word-decreasing self-reducible sets, which are the usual self-reducible sets with the peculiarity that the self-reducibility machine makes at most one query to a word lexicographically smaller than the input. It is first shown that for all counting classes defined by a predicate on the number of accepting paths there exist complete sets which are one-word-decreasing self-redu... View full abstract»

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  • Combinatorics and Kolmogorov complexity

    Publication Year: 1991, Page(s):154 - 163
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (628 KB)

    The authors investigate combinatorial properties of finite sequences with high Kolmogorov complexity. They also demonstrate the utility of a Kolmogorov complexity method in combinatorial theory by several examples (such as the coin-weighing problem).<<ETX>> View full abstract»

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  • The complexity of malign ensembles

    Publication Year: 1991, Page(s):164 - 171
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (494 KB)

    The author analyzes the concept of malignness, which is the property of probability ensembles making the average case running time equal to the worst-case running time for a class of algorithms. He derives lower and upper bounds on the complexity of malign ensembles, which are tight for exponential time algorithms and which show that no polynomial time computable malign ensemble exists for the cla... View full abstract»

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  • Randomized vs. deterministic decision tree complexity for read-once Boolean functions

    Publication Year: 1991, Page(s):172 - 179
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (481 KB)

    The authors consider the deterministic and the randomized decision-tree complexities for Boolean functions, denoted DC(f) and RC(f), respectively. It is well known that RC(f)>or=DC(f)/sup 0.5/ for every Boolean function f (called 0.5-exponent), but no better lower bound is known for all Boolean functions, whereas the best known upper bound is RC(f)= Theta (DC(f)/sup 0//sub .//sup 753 . ./) (or ... View full abstract»

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  • On the Monte Carlo Boolean decision tree complexity of read-once formulae

    Publication Year: 1991, Page(s):180 - 187
    Cited by:  Papers (7)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (498 KB)

    In the Boolean decision tree model there is at least a linear gap between the Monte Carlo and the Las Vegas complexity of a function depending on the error probability. The author proves for a large class of read-once formulae that this trivial speed-up is the best that a Monte Carlo algorithm can achieve. For every formula F belonging to that class it is shown that the Monte Carlo complexity of F... View full abstract»

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  • A pseudorandom oracle characterization of BPP

    Publication Year: 1991, Page(s):190 - 195
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (374 KB)

    It is known from work of C.H. Bennett and J. Gill (1981) and K. Ambos-Spies (1986) that the following conditions are equivalent: (i) L in BPP; (ii); for almost all oracles A, l in P/sup A/. It is shown here that the following conditions are also equivalent to (i) and (ii): (iii) the set of oracles A for which L in P/sup A/ has pspace-measure 1; (iv) for every pspace-random oracle A, L in P/sup A/.... View full abstract»

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  • Notions of resource-bounded category and genericity

    Publication Year: 1991, Page(s):196 - 212
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1117 KB)

    The author investigates the strength of resource-bounded generic sets for deciding results in relativized complexity. He makes technical improvements to J.H. Lutz's notion of resource-bounded Baire category (1987, 1989) to show that almost every exponential-time set (in the author's sense of category) separate P from NP. It is shown that the author's improved notion of category, while strictly mor... View full abstract»

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  • BPP has subexponential time simulations unless EXPTIME has publishable proofs

    Publication Year: 1991, Page(s):213 - 219
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (388 KB)

    It is shown that BPP can be simulated in subexponential time for infinitely many input lengths unless exponential time collapses to the second level of the polynomial-time hierarchy, has polynomial-size circuits, and has publishable proofs (EXPTIME=MA). It is also shown that BPP is contained in subexponential time unless exponential time has publishable proofs for infinitely many input lengths. In... View full abstract»

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  • Relating equivalence and reducibility to sparse sets

    Publication Year: 1991, Page(s):220 - 229
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (661 KB)

    For various polynomial-time reducibilities r, the authors ask whether being r-reducible to a sparse set is a broader notion than being r-equivalent to a sparse set. Although distinguishing equivalence and reducibility to sparse sets, for many-one or 1-truth-table reductions, would imply that P not=NP, the authors show that for k-truth-table reductions, k>or=2, equivalence and reducibility to sp... View full abstract»

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  • Exponential time and subexponential time sets

    Publication Year: 1991, Page(s):230 - 237
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (423 KB)

    The authors prove that the symmetric difference of a <or=/sup P//sub k-parity/-hard set for E and a subexponential time computable set is still <or=P/sub k-parity/-hard for E. This remains true for a <or=/sup P//sub m/-hard set for E since 1-parity reduction is many-one reduction. In addition, it is shown that it is not the case with respect to some other types of reductions. The authors ... View full abstract»

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  • Adaptive logspace and depth-bounded reducibilities

    Publication Year: 1991, Page(s):240 - 254
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1110 KB)

    The author discusses a number of results regarding the study of the computational power of depth-bounded reducibilities, their use to classify the complexity of computational problems, and their characterizations in terms of other computational models. In particular, problems arising in the design of concurrent systems are studied, and two kinds of logarithmic space reductions are defined. The fir... View full abstract»

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