Results 1 
9 of
9
Expander Graphs and their Applications
, 2003
"... Contents 1 The Magical Mystery Tour 7 1.1 Some Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1 Hardness results for linear transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.2 Error Correcting Codes . . . . . . . ..."
Abstract

Cited by 186 (5 self)
 Add to MetaCart
Contents 1 The Magical Mystery Tour 7 1.1 Some Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1 Hardness results for linear transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.2 Error Correcting Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.3 Derandomizing Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Magical Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.1 A Super Concentrator with O(n) edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.2 Error Correcting Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.3 Derandomizing Random Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
NP and Mathematics  a computational complexity perspective
 Proc. of the ICM 06
"... “P versus N P – a gift to mathematics from Computer Science” ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
“P versus N P – a gift to mathematics from Computer Science”
A note on Agrawal conjecture
"... Abstract. We prove that Lenstra proposition suggesting existence of many counterexamples to Agrawal conjecture is true in a more general case. At the same time we obtain a strictly ascending chain of subgroups of the group (Zp[X]/(Cr(X))) * and state the modified conjecture that the set {X1, X+2} ..."
Abstract
 Add to MetaCart
Abstract. We prove that Lenstra proposition suggesting existence of many counterexamples to Agrawal conjecture is true in a more general case. At the same time we obtain a strictly ascending chain of subgroups of the group (Zp[X]/(Cr(X))) * and state the modified conjecture that the set {X1, X+2} generate big enough subgroup of this group. 1
A GENERALIZATION OF MILLER’S PRIMALITY THEOREM PEDRO BERRIZBEITIA AND AURORA OLIVIERI
"... Abstract. For any integer r we show that the notion of ωprime to base a introduced by Berrizbeitia and Berry, 2000, leads to a primality test for numbers n congruent to 1 modulo r, which runs in polynomial time assuming the Extended Riemann Hypothesis (ERH). For r = 2 we obtain Miller’s classical r ..."
Abstract
 Add to MetaCart
Abstract. For any integer r we show that the notion of ωprime to base a introduced by Berrizbeitia and Berry, 2000, leads to a primality test for numbers n congruent to 1 modulo r, which runs in polynomial time assuming the Extended Riemann Hypothesis (ERH). For r = 2 we obtain Miller’s classical result. 1.
Summary
"... Our main aim in the present paper is the extension of the Encryption/Decryption processes using products of primes. We now show in this paper how to generate a group from any general natural number or a product of such natural numbers. We then show how this group can be used for generation of a simp ..."
Abstract
 Add to MetaCart
Our main aim in the present paper is the extension of the Encryption/Decryption processes using products of primes. We now show in this paper how to generate a group from any general natural number or a product of such natural numbers. We then show how this group can be used for generation of a simple (yet as secure, as the one that is generated with the help of larger primes) encryption /decryption process. This work is continuation of the work that the first author had undertaken with Dr. H. Chandrashekhar in the 90’s using Farey Fractions summary.
32
"... A good new millenium for the primes Andrew Granville* is the Canadian Research Chair in number theory at the Université de Montréal. A good new millenium for the primes Prime numbers, the building blocks from which integers are made, are central to much of mathematics. Understanding their distributi ..."
Abstract
 Add to MetaCart
A good new millenium for the primes Andrew Granville* is the Canadian Research Chair in number theory at the Université de Montréal. A good new millenium for the primes Prime numbers, the building blocks from which integers are made, are central to much of mathematics. Understanding their distribution is one of the most natural, and hence oldest, problems in mathematics. Once the ancient Greeks had determined that there are infinitely many then it was natural to ask how many there are up to any given point, perhaps a very large point, how many there are in certain special subsequences (for example, primes of the form “a square plus one”), and how to identify primes quickly. If one examines tables of primes then they appear to be “randomly distributed” though, as Bob Vaughan once put it, “we do not yet know what random means”. Answering these questions has thus proved to be difficult, each success requiring new, far reaching ideas and methods. During the last thirty years there had been few new results of this type but then, in the last decade, several surprises, some of which we will discuss here: