Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)

6-6 May 1999

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  • Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)

    Publication Year: 1999
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    Freely Available from IEEE
  • Pseudorandom generators without the XOR lemma

    Publication Year: 1999
    Cited by:  Papers (28)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (20 KB)

    Summary form only given. R. Impagliazzo and A. Wigderson (1997) have recently shown that if there exists a decision problem solvable in time 2/sup O(n)/ and having circuit complexity 2/sup /spl Omega/(n)/ (for all but finitely many n) then P=BPP. This result is a culmination of a series of works showing connections between the existence of hard predicates and the existence of good pseudorandom gen... View full abstract»

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  • Graph Ramsey theory and the polynomial hierarchy

    Publication Year: 1999
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (15 KB)

    Summary form only given, as follows. In the Ramsey theory of graphs F/spl rarr/(G, H) means that for every way of coloring the edges of F red and blue F will contain either a red G or a blue H as a subgraph. The problem ARROWING of deciding whether F/spl rarr/(G, H) lies in /spl Pi//sub 2//sup P/=coNP/sup NP/ and it was shown to be coNP-hard by S.A. Burr (1990). We prove that ARROWING is actually ... View full abstract»

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  • Author index

    Publication Year: 1999, Page(s): 241
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    Freely Available from IEEE
  • Non-automatizability of bounded-depth Frege proofs

    Publication Year: 1999, Page(s):15 - 23
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (176 KB)

    In this paper; we show how to extend the argument due to Bonet, Pitassi and Raz to show that bounded-depth Frege proofs do not have feasible interpolation, assuming that factoring of Blum integers or computing the Diffie-Hellman function is sufficiently hard. It follows as a corollary that bounded-depth Frege is not automatizable; in other words, there is no deterministic polynomial-time algorithm... View full abstract»

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  • On the complexity of diophantine geometry in low dimensions

    Publication Year: 1999
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (112 KB)

    We consider the average-case complexity of some otherwise undecidable or open Diophantine problems. More precisely, we show that the following two problems can be solved within PSPACE: I. Given polynomials f1,…,fm∈Z[x1 ,…,xn] defining a variety of dimension ⩽0 in Cn, find all solutions in Z View full abstract»

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  • Proofs, codes, and polynomial-time reducibilities

    Publication Year: 1999, Page(s):46 - 53
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (148 KB)

    We show how to construct proof systems for NP languages where a deterministic polynomial-time verifier can check membership, given any N (2/3)+ε bits of an N-bit witness of membership. We also provide a slightly superpolynomial time proof system where the verifier can check membership, given only N(1/2)+ε bits of an N-bit witness. These pursuits are motivated by the... View full abstract»

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  • Query order and NP-completeness

    Publication Year: 1999, Page(s):142 - 148
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (204 KB)

    The effect of query order on NP-completeness is investigated. A sequence D&oarr;=(D1,…,Dk) of decision problems is defined to be sequentially complete for NP if each Di ∈NP and every problem in NP can be decided in polynomial time with one query to each of D1,…,Dk in this order. It is shown that, if NP contains a language th... View full abstract»

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  • Circuit lower bounds collapse relativized complexity classes

    Publication Year: 1999, Page(s):222 - 226
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (124 KB)

    Since the publication of M. Furst et al. (1984) seminal paper connecting AC0 with the polynomial hierarchy, it has been well known that circuit lower bounds allow you to construct oracles that separate complexity classes. We show that similar circuit lower bounds allow you to construct oracles that collapse complexity classes. For example, based on Hastad's parity lower bound, we constr... View full abstract»

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  • A lower bound for primality

    Publication Year: 1999, Page(s):10 - 14
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (172 KB)

    Recent work by Bernasconi, Damm and Shparlinski proved lower bounds on the circuit complexity of the square-free numbers, and raised as an open question if similar (or stronger) lower bounds could be proved for the set of prime numbers. In this short note, we answer this question affirmatively, by showing that the set of prime numbers (represented in the usual binary notation) is not contained in ... View full abstract»

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  • Short proofs are narrow-resolution made simple

    Publication Year: 1999
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (28 KB)

    We develop a general strategy for proving width lower bounds, which follows Haken's original proof technique but is now simple and clear. It reveals that large width is implied by certain natural expansion properties of the clauses (axioms) of the tautology in question. We show that in the classical examples of the Pigeonhole principle, Tseitin graph tautologies, and random k-CNFs, these expansion... View full abstract»

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  • Computing from partial solutions

    Publication Year: 1999, Page(s):34 - 45
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (232 KB)

    We consider the question: Is finding just a part of a solution easier than finding the full solution? For example, is finding only an ε fraction of the bits in a satisfying assignment to a 3-CNF formula easier than computing the whole assignment? For several important problems in NP we show that obtaining only a small fraction of the solution is as hard as finding the full solution. This can ... View full abstract»

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  • De-randomizing BPP: the state of the art

    Publication Year: 1999, Page(s):76 - 77
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (72 KB)

    The introduction of randomization into efficient computation has been one of the most fertile and useful ideas in computer science. In cryptography and asynchronous computing, randomization makes possible tasks that are impossible to perform deterministically. Even for function computation, many examples are known in which randomization allows considerable savings in resources like space and time ... View full abstract»

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  • Complexity of k-SAT

    Publication Year: 1999, Page(s):237 - 240
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (120 KB)

    The problem of k-SAT is to determine if the given k-CNF has a satisfying solution. It is a celebrated open question as to whether it requires exponential time to solve k-SAT for k⩾3. Define sk (for k⩾3) to be the infimum of {δ: there exists an O(2 δn) algorithm for solving k-SAT}. Define ETH (Exponential-Time Hypothesis) for k-SAT as follows: for k⩾3,... View full abstract»

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  • The complexity of solving equations over finite groups

    Publication Year: 1999, Page(s):80 - 86
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (140 KB)

    We study the computational complexity of solving systems of equations over a finite group. An equation over a group G is an expression of the form w1·w2 ·····wk=id where each wi is either a variable, an inverted variable, or group constant and id is the identity element of G. A solution to such an equation is an ... View full abstract»

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  • Gaps in bounded query hierarchies

    Publication Year: 1999, Page(s):124 - 141
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (260 KB)

    Prior results show that most bounded query hierarchies cannot contain finite gaps. For example, it is known that P(m+1)-tt SAT=Pm-ttSAT⇒Pbtt SAT=Pm-ttSAT and for all sets A·FP(m=1)-ttA=FPm-ttA ⇒FPbttA=FPm-ttA View full abstract»

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  • The expected size of Heilbronn's triangles

    Publication Year: 1999, Page(s):105 - 113
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (300 KB)

    Heilbronn's triangle problem asks for the least Δ such that n points lying in the unit disc necessarily contain a triangle of area at most Δ. Heilbronn initially conjectured Δ=O(1/n2 ). As a result of concerted mathematical effort it is currently known that there are positive constants c and C such that c log n/n2⩽Δ⩽C/n8/7-ε for... View full abstract»

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  • Learning DNF by approximating inclusion-exclusion formulae

    Publication Year: 1999, Page(s):215 - 220
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (280 KB)

    We analyze upper and lower bounds on size of Boolean conjunctions necessary and sufficient to approximate a given DNF formula by accuracy slightly better than 1/2 (here we define the size of a Boolean conjunction as the number of distinct variables on which it depends). Such an analysis determines the performance of a naive search algorithm that exhausts Boolean conjunctions in the order of their ... View full abstract»

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  • The communication complexity of pointer chasing. Applications of entropy and sampling

    Publication Year: 1999
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (40 KB)

    The following pointer chasing problem plays a central role in the study of bounded round communication complexity. There are two players A and B. There are two sets of vertices VA and VB of size n each. Player A is given a function fA: VA→VB and player B is given a function fB: VB→VA. In the problem g k the players have to determine ... View full abstract»

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  • Deterministic amplification of space-bounded probabilistic algorithms

    Publication Year: 1999, Page(s):188 - 198
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (212 KB)

    This paper initiates the study of deterministic amplification of space-bounded probabilistic algorithms. The straightforward implementations of known amplification methods cannot be used for such algorithms, since they consume too much space. We present a new implementation of the Ajtai-Komlos-Szemeredi method, that enables to amplify an S-space algorithm that uses r random bits and errs with prob... View full abstract»

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  • On monotone planar circuits

    Publication Year: 1999, Page(s):24 - 31
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (128 KB)

    In this paper we show several results about monotone planar circuits. We show that monotone planar circuits of bounded width, with access to negated input variables, compute exactly the functions in non-uniform AC0. This provides a striking contrast to the non-planar case, where exactly NC1 is computed. We show that the circuit value problem for monotone planar circuits, with... View full abstract»

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  • Comparing entropies in statistical zero knowledge with applications to the structure of SZK

    Publication Year: 1999, Page(s):54 - 73
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (376 KB)

    We consider the following (promise) problem, denoted ED (for Entropy Difference): The input is a pair of circuits, and YES instances (resp., NO instances) are such pairs in which the first (resp., second) circuit generates a distribution with noticeably higher entropy. On one hand we show that any language having a (honest-verifier) statistical zero-knowledge proof is Karp-reducible to ED. On the ... View full abstract»

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  • Quantum bounded query complexity

    Publication Year: 1999, Page(s):149 - 156
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (160 KB)

    We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query, complexity of decision problems. Under traditional complexity assumptions, we obtain an exponential speedup between the quantum and the classical query complexity of function clas... View full abstract»

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  • Complicated complementations

    Publication Year: 1999, Page(s):227 - 236
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (224 KB)

    Kolmogorov complexity has proven to be a very useful tool in simplifying and improving proofs that use complicated combinatorial arguments. Using Kolmogorov complexity for oracle construction, we obtain separation results that are much stronger than separations obtained previously even with the use of very complicated combinatorial arguments. Moreover the use of Kolmogorov arguments almost trivial... View full abstract»

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  • Depth-3 arithmetic formulae over fields of characteristic zero

    Publication Year: 1999, Page(s):87 - 96
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (204 KB)

    In this paper we prove near quadratic lower bounds for depth-3 arithmetic formulae over fields of characteristic zero. Such bounds are obtained for the elementary symmetric functions, the (trace of) iterated matrix multiplication, and the determinant. As corollaries we get the first non-trivial lower bounds for computing polynomials of constant degree, and a gap between the power depth-3 arithmeti... View full abstract»

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