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

June 30 1991-July 3 1991

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Displaying Results 1 - 25 of 39
  • Proceedings of the Sixth Annual Structure in Complexity Theory Conference (Cat. No.91CH3022-1)

    Publication Year: 1991
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    Freely Available from IEEE
  • Monotone separation of logspace from NC1

    Publication Year: 1991, Page(s):294 - 298
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (316 KB)

    It is shown that the monotone analog of logspace computation is more powerful than monotone log-depth circuits: monotone circuits for a certain function in monotone logspace require depth Ω(lg2 n). It is proved that mNC1≠mL . This result shows that the process of pointer jumping, i.e. following a chain of pointers to the end, cannot be simu... 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 (380 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∈BPP; (ii); for almost all oracles A, l∈PA. It is shown here that the following conditions are also equivalent to (i) and (ii): (iii) the set of oracles A for which L∈PA has pspace-mea... 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 (400 KB)

    The authors obtain positive relativization results. In particular, the goal is to prove statements of the kind: `Given two complexity classes C1 and C2, C 1=C2 if and only if for every sparse set S, C1S=C2 S.' The authors derive a sufficient conditi... View full abstract»

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  • Capturing complexity classes by fragments of second order logic

    Publication Year: 1991, Page(s):341 - 352
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (780 KB)

    The expressive power of certain fragments of second-order logic on finite structures is investigated. The fragments are second-order Horn logic, second-order Krom logic, and a symmetric and a deterministic version of the latter. It is shown that all these logics collapse to their existential fragments. In the presence of a successor relation they provide characterizations of polynomial time, deter... View full abstract»

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  • Counting classes are at least as hard as the polynomial-time hierarchy

    Publication Year: 1991, Page(s):2 - 12
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (768 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 computatio... View full abstract»

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  • The perceptron strikes back

    Publication Year: 1991, Page(s):286 - 291
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (404 KB)

    It is shown that every AC0 predicate is computed by a low-degree probabilistic polynomial over the reals. It is demonstrated that circuits composed of a symmetric gate at the root with AND-OR subcircuits of constant depth can be simulated by probabilistic depth-2 circuits with essentially the same symmetric gate at the root and AND gates of small fanin at the bottom. In particular, ever... View full abstract»

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  • Connections between the complexity of unique satisfiability and the threshold behavior of randomized reductions

    Publication Year: 1991, Page(s):255 - 269
    Cited by:  Papers (6)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (924 KB)

    The present research is motivated by new results on the complexity of the unique satisfiability problem (USAT). Some new results are obtained, using the concept of randomized reductions. The proofs use only the fact that USAT is complete for DP under randomized reductions, even though the probability bound of these reductions may be low. Furthermore, the results show that the structural... 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 (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (620 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 yi. A set is random-self-reducible if its characteristic function is. The authors generalize the previous formal definitions of random-self-reducibility. They... View full abstract»

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  • Combinatorics and Kolmogorov complexity

    Publication Year: 1991, Page(s):154 - 163
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (636 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) 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 (504 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 comple... 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 (428 KB)

    The authors prove that the symmetric difference of a ⩽P k-parity-hard set for E and a subexponential time computable set is still ⩽Pk-parity-hard for E. This remains true for a ⩽Pm-hard set for E since 1-parity reduction is many-one reduction. In addition, it is shown that it is not the case with... 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 (1012 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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  • 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 (900 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 PA (resp., NP<... View full abstract»

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  • DSPACE [nk]=VAR[k+1]

    Publication Year: 1991, Page(s):334 - 340
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (424 KB)

    The author proves that the set of properties checkable by a Turing machine in DSPACE[nk] is exactly equal to the set of properties describable by a uniform sequence of first-order sentences using at most k+1 distinct variables. He proves that this is also equal to the set of properties describable using an iterative definition for a finite set of relations of arity View full abstract»

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  • Super-logarithmic depth lower bounds via direct sum in communication complexity

    Publication Year: 1991, Page(s):299 - 304
    Cited by:  Papers (16)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (332 KB)

    The question of whether it is easier to solve two communication problems together rather than separately is related to the complexity of the composition of Boolean functions. Based on this relationship, an approach to separating NC1 from P is outlined. Furthermore, it is shown that the approach provides a new proof of the separation of monotone NC1 ... View full abstract»

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  • Notions of resource-bounded category and genericity

    Publication Year: 1991, Page(s):196 - 212
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1124 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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  • 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 (380 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 View full abstract»

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  • Approximation properties of NP minimization classes

    Publication Year: 1991, Page(s):353 - 366
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1016 KB)

    The authors introduce a novel approach to the logical definability of NP optimization problems by focusing on the expressibility of feasible solutions. They show that in this framework first-order sentences capture exactly all polynomially bounded optimization problems. They also show that, assuming P≠NP, it is an undecidable problem to determine whether a given first-order sentence defines an ... View full abstract»

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  • PP is closed under truth-table reductions

    Publication Year: 1991, Page(s):13 - 15
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (156 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 View full abstract»

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  • Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits

    Publication Year: 1991, Page(s):270 - 284
    Cited by:  Papers (24)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (904 KB)

    The author examines various counting measures on space bounded nondeterministic auxiliary pushdown machines. In the main theorem, it is shown how a NAuxPDA may be simulated efficiently by a uniform family of Boolean circuits, which preserve the number of accepting paths in the NAuxPDA as the number of accepting subtrees in the Boolean circuit. The techniques used simulate the NAuxPDA in a novel wa... 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 (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (432 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 View full abstract»

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  • The complexity of malign ensembles

    Publication Year: 1991, Page(s):164 - 171
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (500 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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  • Adaptive logspace and depth-bounded reducibilities

    Publication Year: 1991, Page(s):240 - 254
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1116 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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  • Superlinear lower bounds for bounded-width branching programs

    Publication Year: 1991, Page(s):305 - 313
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (544 KB)

    The authors use algebraic techniques to obtain superlinear lower bounds on the size of bounded-width branching programs to solve a number of problems. In particular, they show that any bounded-width branching program computing a nonconstant threshold function has length Ω( n log log n), improving on the previous lower bounds known to apply to all such threshold functions. T... View full abstract»

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