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A hard-core predicate for all one-way functions

by Oded Goldreich, Leonid A. Levint - In Proceedings of the Twenty First Annual ACM Symposium on Theory of Computing , 1989
"... Abstract rity of f. In fact, for inputs (to f*) of practical size, the pieces effected by f are so small A central tool in constructing pseudorandom that f can be inverted (and the “hard-core” generators, secure encryption functions, and bit computed) by exhaustive search. in other areas are “hard-c ..."
Abstract - Cited by 440 (5 self) - Add to MetaCart
(within a polynomial) 50) given only f(z). Both b, f are computable security. Namely, we prove a conjecture of in polynomial time. [Levin 87, sec. 5.6.21 that the sca1a.r product [Yao 821 transforms any one-way function of boolean vectors p, x is a hard-core of every f into a more complicated one, f

Genetic Network Inference: From Co-Expression Clustering To Reverse Engineering

by Patrik D'Haeseleer, Shoudan Liang, Roland Somogyi , 2000
"... motivation: Advances in molecular biological, analytical and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using highthroughput gene expression assays, we are able to measure the output of the ge ..."
Abstract - Cited by 336 (0 self) - Add to MetaCart
aspects of clustering, ranging from distance measures to clustering algorithms and multiple-cluster memberships. More advanced analysis aims to infer causal connections between genes directly, i.e. who is regulating whom and how. We discuss several approaches to the problem of reverse engineering

Algebraic Decision Diagrams and their Applications

by R. Iris Bahar, Erica A. Frohm, Charles M. Gaona, Gary D. Hachtel, Enrico Macii, Abelardo Pardo, Fabio Somenzi , 1993
"... In this paper we present theory and experiments on the Algebraic Decision Diagrams (ADD's). These diagrams extend BDD's by allowing values from an arbitrary finite domain to be associated with the terminal nodes. We present a treatment founded in boolean algebras and discuss algorithms and ..."
Abstract - Cited by 321 (18 self) - Add to MetaCart
In this paper we present theory and experiments on the Algebraic Decision Diagrams (ADD's). These diagrams extend BDD's by allowing values from an arbitrary finite domain to be associated with the terminal nodes. We present a treatment founded in boolean algebras and discuss algorithms

Hierarchical classification of Web content

by Susan Dumais , 2000
"... sdumais @ microsoft.com This paper explores the use of hierarchical structure for classifying a large, heterogeneous collection of web content. The hierarchical structure is initially used to train different second-level classifiers. In the hierarchical case, a model is learned to distinguish a seco ..."
Abstract - Cited by 329 (4 self) - Add to MetaCart
models. For the hierarchical approach, we found the same accuracy using a sequential Boolean decision rule and a multiplicative decision rule. Since the sequential approach is much more efficient, requiring only 14%-16 % of the comparisons used in the other approaches, we find it to be a good choice

Multiple Boolean Relations

by Ellen M. Sentovich, Vigyan Singhal, Robert K. Brayton - in Workshop Notes of the Intl. Workshop on Logic Synthesis, (Tahoe City, CA , 1993
"... Flexibility in selecting the Boolean functions to implement a digital circuit has various forms which have been studied in the literature such as don't care conditions, Boolean relations, and synchronous recurrence equations. Each of these represents a particular degree of flexibility that may ..."
Abstract - Cited by 8 (4 self) - Add to MetaCart
be given in the description, inherent in the current representation, or derived from the surrounding environment. This flexibility is used to find an optimal implementation. In this paper, we propose a Multiple Boolean Relation (MBR) as a model that encompasses all degrees of freedom in choosing a set

BOOLEAN ALGEBRA Boolean algebra

by unknown authors
"... or the algebra of logic, was devised by the English mathematician George Boole (1815-64), and embodies the first successful application of algebraic methods to logic. Boole seems initially to have conceived of each of the basic symbols of his algebraic system as standing for the mental operation of ..."
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are interpreted as taking just the number values 0 and 1. In each of these interpretations the basic symbols are conceived as being capable of combination under certain operations: multiplication, corresponding to conjunction of attributes or intersection of classes, addition, corresponding to (exclusive

Circuit Complexity and Multiplicative Complexity of Boolean Functions

by Arist Kojevnikov, Alexander S. Kulikov - IN: PROCEEDINGS OF COMPUTABILITY IN EUROPE (CIE). VOLUME 6158 OF LECTURE NOTES IN COMPUTER SCIENCE , 2010
"... In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3 − c lower bound on the circuit complexity of a large class of functions representable by high degree polynomials over GF(2). The key ide ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3 − c lower bound on the circuit complexity of a large class of functions representable by high degree polynomials over GF(2). The key

On Berge multiplication for monotone boolean dualization

by Endre Boros, Khaled Elbassioni, Kazuhisa Makino
"... Given the prime CNF representation φ of a monotone Boolean function f: {0, 1} n ↦ → {0, 1}, the dualization problem calls for finding the corresponding prime DNF representation ψ of f. A very simple method (called Berge multiplication [3, Page 52–53]) works by multiplying out the clauses of φ from ..."
Abstract - Cited by 3 (0 self) - Add to MetaCart
Given the prime CNF representation φ of a monotone Boolean function f: {0, 1} n ↦ → {0, 1}, the dualization problem calls for finding the corresponding prime DNF representation ψ of f. A very simple method (called Berge multiplication [3, Page 52–53]) works by multiplying out the clauses of φ from

CFG Parsing and Boolean Matrix Multiplication

by Franziska Ebert
"... Abstract. In this work the relation between Boolean Matrix Multipli-cation (BMM) and Context Free Grammar (CFG) parsing is shown. The first described approach, which is due to Valiant (1975), shows how CFG parsing can be reduced to Boolean Matrix Multiplication. Afterwards the reverse direction, i.e ..."
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Abstract. In this work the relation between Boolean Matrix Multipli-cation (BMM) and Context Free Grammar (CFG) parsing is shown. The first described approach, which is due to Valiant (1975), shows how CFG parsing can be reduced to Boolean Matrix Multiplication. Afterwards the reverse direction, i

A Note on Boolean Matrix Multiplication

by Klaus Simon, Paul Trunz , 1995
"... A classical topic in computer science is matrix multiplication and Boolean Matrix Multiplication in particular. Most papers studying these problems present worst case algorithms with running times O(n 2+ff ). For smaller ff these algorithms are rather complex and difficult to understand. As for s ..."
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A classical topic in computer science is matrix multiplication and Boolean Matrix Multiplication in particular. Most papers studying these problems present worst case algorithms with running times O(n 2+ff ). For smaller ff these algorithms are rather complex and difficult to understand
Results 1 - 10 of 882