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Computational Complexity, 1997. Proceedings., Twelfth Annual IEEE Conference on (Formerly: Structure in Complexity Theory Conference)

Date 24-27 June 1997

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  • Proceedings of Computational Complexity. Twelfth Annual IEEE Conference

    Publication Year: 1997
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    Freely Available from IEEE
  • Author index

    Publication Year: 1997, Page(s): 315
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    Freely Available from IEEE
  • Inequalities for Shannon entropies and Kolmogorov complexities

    Publication Year: 1997, Page(s):13 - 23
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (772 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... View full abstract»

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  • Circuits over PP and PL

    Publication Year: 1997, Page(s):24 - 35
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (676 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 NC1 reductions. This answers an open problem of M. Ogihara (1996). More generally, we show that NCk+1PP=ACk... 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 (680 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·. 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 class d... View full abstract»

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  • Finite limits and monotone computations: the lower bounds criterion

    Publication Year: 1997, Page(s):302 - 313
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1008 KB)

    Our main result is a combinatorial lower bounds criterion for monotone circuits over the reals. We allow any unbounded fanin non-decreasing real-valued functions as gates. The only requirement is their “locality”. Unbounded fanin AND and OR gates, as well as any threshold gate Tsm(x1,...,xm) with small enough threshold value min{s,m-s+1}, are... View full abstract»

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  • Reversible space equals deterministic space

    Publication Year: 1997, Page(s):45 - 50
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (516 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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  • 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 (832 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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  • On TC0, AC0, and arithmetic circuits

    Publication Year: 1997, Page(s):134 - 148
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1112 KB)

    Continuing a line of investigation that has studied the function classes P, we study the class of functions AC0. One way to define AC0 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, lowe... View full abstract»

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  • Six hypotheses in search of a theorem

    Publication Year: 1997, Page(s):2 - 12
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (816 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||NP =FPNP[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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  • The communication complexity of the universal relation

    Publication Year: 1997, Page(s):247 - 259
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (996 KB)

    Consider the following communication problem. Alice gets a word x∈{0,1}n and Bob gets a word y∈{0,1}n. Alice and Bob are told that x≠y. Their goal is to find an index 1⩽i⩽n such that xi≠yi (the index i should be known to both of them). This problem is one of the most basic communication problems. It arises naturally from the corre... View full abstract»

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  • Constraint satisfaction: the approximability of minimization problems

    Publication Year: 1997, Page(s):282 - 296
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1568 KB)

    This paper continues the work initiated by N. Creignou (1995) and S. Khanna et al. (1997) who classify maximization problems derived from Boolean constraint satisfaction. We study the approximability of minimization problems derived thence. A problem in this framework is characterized by a collection F of “constraints” (i.e., functions f: {0,1}k→{0,1}) and an instance o... 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 (596 KB)

    Given a real number α<1, every language that is weakly ⩽nα/2-TP-hard for E or weakly ⩽nα-TP-hard for E2 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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  • 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 (580 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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  • 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 (476 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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  • A note on the bottleneck counting argument

    Publication Year: 1997, Page(s):297 - 301
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (436 KB)

    Both the bottleneck counting argument and Razborov's approximation method have been used to prove exponential lower bounds for monotone circuits. We show that under the monotone circuit model for every proof by the approximation method, there is a bottleneck counting proof and vice versa. We also illustrate the elegance of the bottleneck counting technique with a simple self-explained example: the... 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 (376 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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  • Nondeterministic polynomial time versus nondeterministic logarithmic space: time-space tradeoffs for satisfiability

    Publication Year: 1997, Page(s):52 - 60
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (684 KB)

    We give the first nontrivial model-independent time-space tradeoffs for satisfiability. Namely, we show that S¯A¯T¯ cannot be solved simultaneously in n1+0(1) time and n1-ε space for any ε>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 S&... View full abstract»

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  • Randomized simultaneous messages: solution of a problem of Yao in communication complexity

    Publication Year: 1997, Page(s):239 - 246
    Cited by:  Papers (3)  |  Patents (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (620 KB)

    We solve a 17 year old problem of A.C.C. Yao (1979). In the two-player communication model introduced by Yao in 1979, Alice and Bob wish to collaboratively evaluate a function f(x,y) in which Alice knows only input x and Bob knows only input y. Both players have unlimited computational power. The objective is to minimize the amount of communication. Yao (1979) also introduced an oblivious version ... 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 (796 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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  • 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 (672 KB)

    We investigate the complexity of depth-3 threshold circuits with majority gates at the output, possibly negated AND gates at level two, and MODm 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 t... View full abstract»

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  • Circuits and expressions with non-associative gates

    Publication Year: 1997, Page(s):193 - 203
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (868 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 short guide to approximation preserving reductions

    Publication Year: 1997, Page(s):262 - 273
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1012 KB)

    Comparing the complexity of different combinatorial optimization problems has been an extremely active research area during the last 23 years. This has led to the definition of several approximation preserving reducibilities and to the development of powerful reduction techniques. We first review the main approximation preserving reducibilities that have appeared in the literature and suggest whic... 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 (764 KB)

    Assuming that the polynomial hierarchy (PH) does not collapse, we show the existence of ascending sequences of ptime Turing degrees of length ω1CK 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 degr... View full abstract»

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  • On randomization in online computation

    Publication Year: 1997, Page(s):226 - 238
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1188 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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