Results 1  10
of
1,219,568
DepthIndependent Lower bounds on the Communication Complexity of ReadOnce Boolean Formulas
, 908
"... We show lower bounds of Ω ( √ n) and Ω(n 1/4) on the randomized and quantum communication complexity, respectively, of all nvariable readonce Boolean formulas. Our results complement the recent lower bound of Ω(n/8 d) by Leonardos and Saks [LS09] and Ω(n/2 Ω(d log d)) by Jayram, Kopparty and Ragh ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We show lower bounds of Ω ( √ n) and Ω(n 1/4) on the randomized and quantum communication complexity, respectively, of all nvariable readonce Boolean formulas. Our results complement the recent lower bound of Ω(n/8 d) by Leonardos and Saks [LS09] and Ω(n/2 Ω(d log d)) by Jayram, Kopparty
On the Communication Complexity of ReadOnce AC 0 Formulae
"... Abstract—We study the 2party randomized communication complexity of readonce AC 0 formulae. For balanced ANDOR trees T with n inputs and depth d, we show that the communication complexity of the function f T (x, y) = T (x◦y) is Ω(n/4 d) where (x◦y)i is defined so that the resulting tree also has ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Abstract—We study the 2party randomized communication complexity of readonce AC 0 formulae. For balanced ANDOR trees T with n inputs and depth d, we show that the communication complexity of the function f T (x, y) = T (x◦y) is Ω(n/4 d) where (x◦y)i is defined so that the resulting tree also
A Lower Bound for Integer Multiplication on Randomized ReadOnce Branching Programs
, 1998
"... We prove an exponential lower bound (2\Omega\Gamma n= log n) ) on the size of any randomized ordered readonce branching program computing integer multiplication. Our proof depends on proving a new lower bound on Yao's randomized oneway communication complexity of certain boolean functions. ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
We prove an exponential lower bound (2\Omega\Gamma n= log n) ) on the size of any randomized ordered readonce branching program computing integer multiplication. Our proof depends on proving a new lower bound on Yao's randomized oneway communication complexity of certain boolean functions
Multiparty Communication Complexity
, 1989
"... A given Boolean function has its input distributed among many parties. The aim is to determine which parties to tMk to and what information to exchange with each of them in order to evaluate the function while minimizing the total communication. This paper shows that it is possible to obtain the Boo ..."
Abstract

Cited by 764 (22 self)
 Add to MetaCart
the Boolean answer deterministically with only a polynomial increase in communication with respect to the information lower bound given by the nondeterministic communication complexity of the function.
Monotone Complexity
, 1990
"... We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a simple ..."
Abstract

Cited by 2837 (11 self)
 Add to MetaCart
We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a
Learning ReadOnce Formulas with Queries
 J. ACM
, 1989
"... A readonce formula is a boolean formula in which each variable occurs at most once. Such formulas are also called ¯formulas or boolean trees. This paper treats the problem of exactly identifying an unknown readonce formula using specific kinds of queries. The main results are a polynomial time al ..."
Abstract

Cited by 117 (19 self)
 Add to MetaCart
A readonce formula is a boolean formula in which each variable occurs at most once. Such formulas are also called ¯formulas or boolean trees. This paper treats the problem of exactly identifying an unknown readonce formula using specific kinds of queries. The main results are a polynomial time
Wireless Communications
, 2005
"... Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University ..."
Abstract

Cited by 1129 (32 self)
 Add to MetaCart
Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University
Randomized Algorithms
, 1995
"... Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available, or the simp ..."
Abstract

Cited by 2210 (37 self)
 Add to MetaCart
Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available
Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
Abstract

Cited by 2083 (10 self)
 Add to MetaCart
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled
Results 1  10
of
1,219,568