Proceedings of Computational Complexity. Twelfth Annual IEEE Conference

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
  • 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 (968 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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  • A lower bound for perceptrons and an oracle separation of the PP PH hierarchy

    Publication Year: 1997, Page(s):165 - 172
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (676 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 Σkp,A⊄PPΣ(k-2 p,A) and in particular this oracle separates the levels in the PPPH... 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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  • 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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  • 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 (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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  • 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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  • 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 (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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  • 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 (436 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(nk). The result is based on the fact that there exists an enumeration of the O(nk)-time ... 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 (604 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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  • Randomized simultaneous messages: solution of a problem of Yao in communication complexity

    Publication Year: 1997, Page(s):239 - 246
    Cited by:  Papers (8)  |  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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  • 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 (480 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⊇(m+1, m+d+1) P for m<2d; and 2) (m, m+d) P=(m+1, m+d+1) P for m⩾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 exis... 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 (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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  • 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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  • 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 (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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  • 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 (760 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 Ω(n1+1k//log n) to compute several natural families of functions, including sorting, finite field arithmetic, and the “rigid linear tr... 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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  • 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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  • Tight bound on Johnson's algorithm for Max-SAT

    Publication Year: 1997, Page(s):274 - 281
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (616 KB)

    We present a new technique that gives a more thorough analysis on Johnson's classical algorithm for the maximum satisfiability problem. In contrast to the common belief for two decades that Johnson's algorithm has performance ratio 1/2, we show that the performance ratio is 2/3, and that this bound is tight. Moreover we show that simple generalizations of Johnson's algorithm do not improve the per... 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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  • 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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  • 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 (1880 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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  • Inequalities for Shannon entropies and Kolmogorov complexities

    Publication Year: 1997, Page(s):13 - 23
    Cited by:  Papers (4)
    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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