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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»
14 years 4 months 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
15 years 3 months 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
15 years 1 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»
15 years 6 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»
15 years 1 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