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2009
Springer

Faster real feasibility via circuit discriminants

12 years 8 months ago
Faster real feasibility via circuit discriminants
We show that detecting real roots for honestly n-variate (n + 2)-nomials (with integer exponents and coefficients) can be done in time polynomial in the sparse encoding for any fixed n. The best previous complexity bounds were exponential in the sparse encoding, even for n fixed. We then give a characterization of those functions k(n) such that the complexity of detecting real roots for n-variate (n + k(n))-nomials transitions from P to NP-hardness as n −→ ∞. Our proofs follow in large part from a new complexity threshold for deciding the vanishing of A-discriminants of n-variate (n+k(n))-nomials. Diophantine approximation, through linear forms in logarithms, also arises as a key tool. Keywords sparse, real, feasibility, polynomial-time, discriminant chamber, linear forms in logarithms
Frédéric Bihan, J. Maurice Rojas, Ca
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where ISSAC
Authors Frédéric Bihan, J. Maurice Rojas, Casey E. Stella
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