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» On the Degree of Univariate Polynomials Over the Integers
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CORR
2011
Springer
158views Education» more  CORR 2011»
13 years 23 days ago
SqFreeEVAL: An (almost) optimal real-root isolation algorithm
Let f be a univariate polynomial with real coefficients, f ∈ R[X]. Subdivision algorithms based on algebraic techniques (e.g., Sturm or Descartes methods) are widely used for is...
Michael Burr, Felix Krahmer
TPHOL
2007
IEEE
14 years 22 hour ago
Verifying Nonlinear Real Formulas Via Sums of Squares
Techniques based on sums of squares appear promising as a general approach to the universal theory of reals with addition and multiplication, i.e. verifying Boolean combinations of...
John Harrison
FOCS
2007
IEEE
13 years 9 months ago
Discrepancy and the Power of Bottom Fan-in in Depth-three Circuits
We develop a new technique of proving lower bounds for the randomized communication complexity of boolean functions in the multiparty `Number on the Forehead' model. Our meth...
Arkadev Chattopadhyay
STOC
2010
ACM
168views Algorithms» more  STOC 2010»
14 years 3 months ago
Non-commutative circuits and the sum-of-squares problem
We initiate a direction for proving lower bounds on the size of non-commutative arithmetic circuits. This direction is based on a connection between lower bounds on the size of no...
Pavel Hrubes, Avi Wigderson and Amir Yehudayoff
ANTS
2006
Springer
93views Algorithms» more  ANTS 2006»
13 years 9 months ago
Testing Equivalence of Ternary Cubics
Let C be a smooth plane cubic curve with Jacobian E. We give a formula for the action of the 3-torsion of E on C, and explain how it is useful in studying the 3-Selmer group of an ...
Tom Fisher