Results 1 - 10 of 919

Iterated Forcing with ${}^{\omega}\omega$-bounding and Semiproper Preorders

by Tadatoshi Miyamoto
"... Assume the Continuum Hypothesis (CH) in the ground model. If we iteratively force with preorders which are $\omega\omega$-bounding and semiproper taking suitable limits, then so is the final preorder constructed. Therefore we may show that the Cofinal Branch Principle (CBP) of [F] is strictly weaker ..."
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Assume the Continuum Hypothesis (CH) in the ground model. If we iteratively force with preorders which are $\omega\omega$-bounding and semiproper taking suitable limits, then so is the final preorder constructed. Therefore we may show that the Cofinal Branch Principle (CBP) of [F] is strictly

Lower Bounds for Discrete Logarithms and Related Problems

by Victor Shoup , 1997
"... . This paper considers the computational complexity of the discrete logarithm and related problems in the context of "generic algorithms"---that is, algorithms which do not exploit any special properties of the encodings of group elements, other than the property that each group element is ..."
Abstract - Cited by 288 (11 self) - Add to MetaCart
is encoded as a unique binary string. Lower bounds on the complexity of these problems are proved that match the known upper bounds: any generic algorithm must perform\Omega (p 1=2 ) group operations, where p is the largest prime dividing the order of the group. Also, a new method for correcting a faulty

Decoding Reed Solomon Codes beyond the Error-Correction Bound

by Madhu Sudan , 1997
"... We present a randomized algorithm which takes as input n distinct points f(xi; yi)g n i=1 from F \Theta F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points in a ..."
Abstract - Cited by 274 (18 self) - Add to MetaCart
in at least t places (i.e., yi = f (xi) for at least t values of i), provided t = \Omega (

Maintaining Stream Statistics over Sliding Windows (Extended Abstract)

by Mayur Datar, Aristides Gionis, Piotr Indyk, Rajeev Motwani , 2002
"... We consider the problem of maintaining aggregates and statistics over data streams, with respect to the last N data elements seen so far. We refer to this model as the sliding window model. We consider the following basic problem: Given a stream of bits, maintain a count of the number of 1's i ..."
Abstract - Cited by 269 (9 self) - Add to MetaCart
;s in the last N elements seen from the stream. We show that using O( 1 ffl log 2 N) bits of memory, we can estimate the number of 1's to within a factor of 1 + ffl. We also give a matching lower bound of \Omega\Gamma 1 ffl log 2 N) memory bits for any deterministic or randomized algorithms. We

Which Problems Have Strongly Exponential Complexity?

by Russell Impagliazzo, Ramamohan Paturi, Francis Zane - Journal of Computer and System Sciences , 1998
"... For several NP-complete problems, there have been a progression of better but still exponential algorithms. In this paper, we address the relative likelihood of sub-exponential algorithms for these problems. We introduce a generalized reduction which we call Sub-Exponential Reduction Family (SERF) t ..."
Abstract - Cited by 242 (11 self) - Add to MetaCart
formulas whose first order part is universal. In particular, sub-exponential complexity for any one of the above problems implies the same for all others. We also look at the issue of proving strongly exponential lower bounds for AC 0 ; that is, bounds of the form 2 \Omega\Gamma n) . This problem

Adaptive Finite Element Methods For Parabolic Problems. VI. Analytic Semigroups

by Kenneth Eriksson, Claes Johnson, Stig Larsson - SIAM J. Numer. Anal , 1998
"... . We continue our work on adaptive finite element methods with a study of time discretization of analytic semigroups. We prove optimal a priori and a posteriori error estimates for the discontinuous Galerkin method showing, in particular, that analytic semigroups allow long-time integration without ..."
Abstract - Cited by 215 (3 self) - Add to MetaCart
) = u 0 ; (1.1) where H = L 2 (\Omega\Gamma with\Omega a bounded domain in R n , Av = ...

Dynamic Perfect Hashing: Upper and Lower Bounds

by Martin Dietzfelbinger, Anna Karlin, Kurt Mehlhorn, Friedhelm Meyer auf der Heide, Hans Rohnert, Robert E. Tarjan , 1990
"... The dynamic dictionary problem is considered: provide an algorithm for storing a dynamic set, allowing the operations insert, delete, and lookup. A dynamic perfect hashing strategy is given: a randomized algorithm for the dynamic dictionary problem that takes O(1) worst-case time for lookups and ..."
Abstract - Cited by 140 (14 self) - Add to MetaCart
and O(1) amortized expected time for insertions and deletions; it uses space proportional to the size of the set stored. Furthermore, lower bounds for the time complexity of a class of deterministic algorithms for the dictionary problem are proved. This class encompasses realistic hashing

Optimal Bounds for Transformations of ω-Automata

by Christof Löding , 1999
"... In this paper we settle the complexity of some basic constructions of omega-automata theory, concerning transformations of automata characterizing the set of omega-regular languages. In particular we consider Safra's construction (for the conversion of nondeterministic Büchi automata into deter ..."
Abstract - Cited by 22 (0 self) - Add to MetaCart
In this paper we settle the complexity of some basic constructions of omega-automata theory, concerning transformations of automata characterizing the set of omega-regular languages. In particular we consider Safra's construction (for the conversion of nondeterministic Büchi automata

Concurrent Omega-Regular Games

by Luca de Alfaro, Thomas A. Henzinger , 2000
"... We consider two-player games which are played on a finite state space for an infinite number of rounds. The games are concurrent, that is, in each round, the two players choose their moves independently and simultaneously; the current state and the two moves determine a successor state. We consider ..."
Abstract - Cited by 42 (12 self) - Add to MetaCart
omega-regular winning conditions on the resulting infinite state sequence. To model the independent choice of moves, both players are allowed to use randomization for selecting their moves. This gives rise to the following qualitative modes of winning, which can be studied without numerical

Zero Knowledge and the Chromatic Number

by Uriel Feige, Joe Kilian - Journal of Computer and System Sciences , 1996
"... We present a new technique, inspired by zero-knowledge proof systems, for proving lower bounds on approximating the chromatic number of a graph. To illustrate this technique we present simple reductions from max-3-coloring and max-3-sat, showing that it is hard to approximate the chromatic number wi ..."
Abstract - Cited by 196 (6 self) - Add to MetaCart
We present a new technique, inspired by zero-knowledge proof systems, for proving lower bounds on approximating the chromatic number of a graph. To illustrate this technique we present simple reductions from max-3-coloring and max-3-sat, showing that it is hard to approximate the chromatic number
Results 1 - 10 of 919