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Proceedings of Computational Complexity. Twelfth Annual IEEE Conference

24-27 June 1997

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Displaying Results 1 - 25 of 33
  • Proceedings of Computational Complexity. Twelfth Annual IEEE Conference

    Publication Year: 1997
    Request permission for commercial reuse | PDF file iconPDF (424 KB)
    Freely Available from IEEE
  • Six hypotheses in search of a theorem

    Publication Year: 1997, Page(s):2 - 12
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (909 KB)

    We consider the following six hypotheses: *P=NP. *SAT is truth-table reducible to a P-selective set. *SAT is truth-table reducible to a k-approximable set for some k. *FP/sub /spl par///sup NP/=FP/sup NP[log]/ *SAT is O(log n)-approximable. *Solving SAT is in P on formulae with at most one assignment. We discuss their importance and relationships among them. View full abstract»

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  • Inequalities for Shannon entropies and Kolmogorov complexities

    Publication Year: 1997, Page(s):13 - 23
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (858 KB)

    Since the very beginning the notion of complexity of finite objects was considered as an algorithmic counterpart to the notion of Shannon entropy. Kolmogorov's paper (1965) was called "Three approaches to the quantitative definition of information"; Shannon entropy and algorithmic complexity were among these approaches. It was mentioned by Kolmogorov later (1968) that the properties of algorithmic... View full abstract»

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  • Circuits over PP and PL

    Publication Year: 1997, Page(s):24 - 35
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (771 KB)

    C.B. Wilson's (1985) model of oracle gates provides a framework for considering reductions whose strength is intermediate between truth-table and Turing. Improving on a stream of results by previous authors, we prove that PL and PP are closed under NC/sub 1/ reductions. This answers an open problem of M. Ogihara (1996). More generally, we show that NC/sub k+1//sup PP/=AC/sub k//sup PP/ and NC/sub ... View full abstract»

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  • The general notion of a dot-operator

    Publication Year: 1997, Page(s):36 - 44
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (765 KB)

    Well-known examples of dot-operators are the existential, the counting, and the BP-operator. We will generalize this notion of a dot-operator so that every language A will determine an operator A/spl middot/. In fact we will introduce the more general notion of promise dot-operators for which the BP-operator is an example. Dot-operators are a refinement of the leaf language concept because the cla... View full abstract»

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  • Reversible space equals deterministic space

    Publication Year: 1997, Page(s):45 - 50
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (581 KB)

    This paper describes the simulation of an S(n) space-bounded deterministic Turing machine by a reversible Turing machine operating in space S(n). It thus answers a question posed by C. Bennett (1989) and refutes the conjecture, made by M. Li and P. Vitanyi (1996), that any reversible simulation of an irreversible computation must obey Bennett's reversible pebble game rules. View full abstract»

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  • Nondeterministic polynomial time versus nondeterministic logarithmic space: time-space tradeoffs for satisfiability

    Publication Year: 1997, Page(s):52 - 60
    Cited by:  Papers (17)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (758 KB)

    We give the first nontrivial model-independent time-space tradeoffs for satisfiability. Namely, we show that SAT cannot be solved simultaneously in n/sup 1+0(1)/ time and n/sup 1-/spl epsiv// space for any /spl epsiv/>0 on general random-access nondeterministic Turing machines. We also give several other related results. Our proof uses two basic ideas. First we show that if SAT can be solved no... View full abstract»

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  • Polynomial vicinity circuits and nonlinear lower bounds

    Publication Year: 1997, Page(s):61 - 68
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (867 KB)

    We study families of Boolean circuits with the property that the number of gates at distance t fanning into or out of any given gate in a circuit is bounded above by a polynomial in t of some degree k. We prove that such circuits require size /spl Omega/(n/sup 1+1/k//log n) to compute several natural families of functions, including sorting, finite field arithmetic, and the "rigid linear transform... View full abstract»

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  • A note on universal distributions for polynomial-time computable distributions

    Publication Year: 1997, Page(s):69 - 73
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (496 KB)

    Polynomial-time computable as well as polynomial-time samplable distributions play a central role in the theory of average-case complexity. It is known that for every constant k there are polynomial-time samplable distributions which dominate every distribution that is samplable in time O(n/sup k/). The result is based on the fact that there exists an enumeration of the O(n/sup k/)-time samplable ... View full abstract»

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  • LR(k) testing is average case complete

    Publication Year: 1997, Page(s):74 - 80
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (546 KB)

    In this note, we show that LR(k) testing of context free grammars with respect to random instances is many-one complete for Distributional NP. The same result holds for testing whether a context free grammar is LL(k), strong LL(k), SLR(k), LC(k) or strong LC(k), respectively. View full abstract»

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  • Complexity and expressive power of logic programming

    Publication Year: 1997, Page(s):82 - 101
    Cited by:  Papers (14)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2077 KB)

    This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important ext... View full abstract»

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  • Hyper-polynomial hierarchies and the NP-jump

    Publication Year: 1997, Page(s):102 - 110
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (870 KB)

    Assuming that the polynomial hierarchy (PH) does not collapse, we show the existence of ascending sequences of ptime Turing degrees of length /spl omega//sub 1//sup CK/ all of which are in PSPACE and uniformly hard for PH, such that successors are NP-jumps of their predecessors. This is analogous to the hyperarithmetic hierarchy which is defined similarly but with the (recursive) Turing degrees. T... View full abstract»

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  • The density of weakly complete problems under adaptive reductions

    Publication Year: 1997, Page(s):111 - 120
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (679 KB)

    Given a real number /spl alpha/<1, every language that is weakly /spl les//sub n/spl alpha//2-T//sup P/-hard for E or weakly /spl les//sub n/spl alpha/-T//sup P/-hard for E/sub 2/ is shown to be exponentially dense. This simultaneously strengthens results of J.H. Lutz and E. Mayordomo (1994) and B. Fu (1995). View full abstract»

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  • Separating NP-completeness notions under strong hypotheses

    Publication Year: 1997, Page(s):121 - 127
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (684 KB)

    J.H. Lutz (1993) proposed the study of the structure of the class NP=NTIME(poly) under the hypothesis that NP does not have p-measure 0 (with respect to Lutz's resource bounded measure. J.H. Lutz and E. Mayordomo (1996) showed that, under this hypothesis, NP-m-completeness and NP-T-completeness differ and they conjectured that further NP-completeness notions can be separated. Here we prove this co... View full abstract»

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  • Undecidability results for low complexity degree structures

    Publication Year: 1997, Page(s):128 - 132
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (429 KB)

    We prove that the theory of EXPTIME degrees with respect to polynomial time Turing and many-one reducibility is undecidable. To do so we use a coding method based on ideal lattices of Boolean algebras which is introduced A. Nies. The method can be applied in fact to all hyper-polynomial time classes. View full abstract»

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  • On TC/sup 0/, AC/sup 0/, and arithmetic circuits

    Publication Year: 1997, Page(s):134 - 148
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1242 KB)

    Continuing a line of investigation that has studied the function classes P, we study the class of functions AC/sup 0/. One way to define AC/sup 0/ is as the class of functions computed by constant-depth polynomial-size arithmetic circuits of unbounded fanin addition and multiplication gates. In contrast to the preceding function classes, for which we know no nontrivial lower bounds, lower bounds f... View full abstract»

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  • Upper and lower bounds for some depth-3 circuit classes

    Publication Year: 1997, Page(s):149 - 157
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (759 KB)

    We investigate the complexity of depth-3 threshold circuits with majority gates at the output, possibly negated AND gates at level two, and MOD/sub m/ gates at level one. We show that the fan-in of the AND gates can be reduced to O(log n) in the case where m is unbounded, and to a constant in the case where m is constant. We then use these upper bounds to derive exponential lower bounds for this c... View full abstract»

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  • Circuit bottom fan-in and computational power

    Publication Year: 1997, Page(s):158 - 164
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (653 KB)

    We investigate the relationship between circuit bottom fan-in and circuit size when circuit depth is fixed. We show that in order to compute certain functions, a moderate reduction in circuit bottom fan-in will cause significant increase in circuit size. In particular, we prove that there are functions that are computable by circuits of linear size and depth k with bottom fan-in 2 but require expo... View full abstract»

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  • A lower bound for perceptrons and an oracle separation of the PP/sup PH/ hierarchy

    Publication Year: 1997, Page(s):165 - 172
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (755 KB)

    We show that there are functions computable by linear size boolean circuits of depth k that require superpolynomial size perceptrons of depth k-1, for k<log n/(6 log log n). This result implies the existence of an oracle A such that /spl Sigma//sub k//sup p,A//spl nsub/PP/sup /spl Sigma//(/sub k-2//sup p,A/) and in particular this oracle separates the levels in the PP/sup PH/ hierarchy. Using t... View full abstract»

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  • On operators of higher types

    Publication Year: 1997, Page(s):174 - 184
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (895 KB)

    We discuss the use of operators of higher types in complexity theory. These are operators ranging over sets of words, i.e. over oracles. Depending on different oracle access mechanisms we consider two types of operators. In particular we examine existential, universal, and bounded-error probabilistic operators. We identify some of the emerging classes and we interpret recent results about interact... View full abstract»

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  • Time bounded frequency computations

    Publication Year: 1997, Page(s):185 - 192
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (556 KB)

    First we obtain two new results considering the inclusion problem of polynomial time frequency classes with equal numbers of errors: 1) (m, m+d) P/spl supe/(m+1, m+d+1) P for m<2/sup d/; and 2) (m, m+d) P=(m+1, m+d+1) P for m/spl ges/c(d) where c(d) is large enough. This disproves a conjecture of Kinber (1975). Next we give a transparent proof of a generalization of Kinber's result that there e... View full abstract»

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  • Circuits and expressions with non-associative gates

    Publication Year: 1997, Page(s):193 - 203
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (975 KB)

    We consider circuits and expressions whose gates carry out multiplication in a non-associative groupoid such as loop. We define a class we call the polyabelian groupoids, formed by iterated quasidirect products of Abelian groups. We show that a loop can express arbitrary Boolean functions if and only if it is not polyabelian, in which case its EXPRESSION EVALUATION and CIRCUIT VALUE problems are N... View full abstract»

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  • A nonadaptive NC checker for permutation group intersection

    Publication Year: 1997, Page(s):204 - 212
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (938 KB)

    In this paper we design a nonadaptive NC checker for permutation group intersection, sharpening a result from M. Blum and S. Kannan (1995). This is a consequence of two results. First we show that a nontrivial permutation in the intersection of two given permutation groups (described by lists of generators) can be computed by an NC algorithm with one round of parallel queries to the group intersec... View full abstract»

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  • Acceptance by transformation monoids (with an application to local self reductions)

    Publication Year: 1997, Page(s):213 - 224
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1089 KB)

    We study the power of transformation monoids, which are used as an acceptance mechanism of nondeterministic polynomial time machines. Focussing our attention on four types of transformation monoids (including the monoids of all transformations on k elements) we obtain exact characterizations of all investigated polynomial time classes. We apply these results to the cases of locally self reducible ... View full abstract»

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  • On randomization in online computation

    Publication Year: 1997, Page(s):226 - 238
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1328 KB)

    This paper concerns two fundamental but somewhat neglected issues both related to the design and analysis of randomized online algorithms. Motivated by early results in game theory we define several types of randomized online algorithms discuss known conditions for their equivalence and give a natural example distinguishing between two kinds of randomizations. In particular we show that mixed rand... View full abstract»

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