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» On Equations over Sets of Integers
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MST
2011
244views Hardware» more  MST 2011»
12 years 12 months ago
Complexity of Equations over Sets of Natural Numbers
Artur Jez, Alexander Okhotin
FFA
2008
75views more  FFA 2008»
13 years 5 months ago
Syntactical and automatic properties of sets of polynomials over finite fields
Syntactical properties of representations of integers in various number systems are well-known and have been extensively studied. In this paper, we transpose the notion of recogniz...
Michel Rigo
CHES
2005
Springer
155views Cryptology» more  CHES 2005»
13 years 11 months ago
Scalable Hardware for Sparse Systems of Linear Equations, with Applications to Integer Factorization
Motivated by the goal of factoring large integers using the Number Field Sieve, several special-purpose hardware designs have been recently proposed for solving large sparse system...
Willi Geiselmann, Adi Shamir, Rainer Steinwandt, E...
FOCS
2009
IEEE
14 years 3 days ago
Linear Systems over Composite Moduli
We study solution sets to systems of generalized linear equations of the form ℓi(x1, x2, · · · , xn) ∈ Ai (mod m) where ℓ1, . . . , ℓt are linear forms in n Boolean var...
Arkadev Chattopadhyay, Avi Wigderson
TIT
2008
75views more  TIT 2008»
13 years 5 months ago
Linear Network Codes and Systems of Polynomial Equations
If and are nonnegative integers and F is a field, then a polynomial collection {p1, . . . , p} Z[1, . . . , ] is said to be solvable over F if there exist 1, . . . , F such t...
Randall Dougherty, Christopher F. Freiling, Kennet...