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Electronic Colloquium on Computational Complexity

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Reports tagged with linear programming duality:
TR13-023 | 6th February 2013
Alexander A. Sherstov

Approximating the AND-OR Tree

The approximate degree of a Boolean function $f$ is the least degree of a real polynomial
that approximates $f$ within $1/3$ at every point. We prove that the function $\bigwedge_{i=1}^{n}\bigvee_{j=1}^{n}x_{ij}$,
known as the AND-OR tree, has approximate degree $\Omega(n).$ This lower bound is tight
and closes a ... more >>>

TR13-032 | 26th February 2013
Mark Bun, Justin Thaler

Dual Lower Bounds for Approximate Degree and Markov-Bernstein Inequalities

Revisions: 2

The $\epsilon$-approximate degree of a Boolean function $f: \{-1, 1\}^n \to \{-1, 1\}$ is the minimum degree of a real polynomial that approximates $f$ to within $\epsilon$ in the $\ell_\infty$ norm. We prove several lower bounds on this important complexity measure by explicitly constructing solutions to the dual of an ... more >>>

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