Ilias Diakonikolas

Testing for Concise Representations

We describe a general method for testing whether a function on n input variables has a concise representation. The approach combines ideas from the junta test of Fischer et al. 16 with ideas from learning theory, and yields property testers that make po!y(s/epsiv) queries (independent of n) for Boolean function classes such as s-term DNF formulas (answering a question posed by Parnas et al. [12]), sizes. decision trees, sizes Boolean formulas, and sizes Boolean circuits. The method can be applied to non-Boolean valued function classes as well. This is achieved via a generalization of the notion of van at ion/row Fischer et al. to non-Boolean functions. Using this generalization we extend the original junta test of Fischer et al. to work for non-Boolean functions, and give poly(s/e)-query testing algorithms for non-Boolean valued function classes such as sizes algebraic circuits and s-sparse polynomials over finite fields. We also prove an Omega(radic(s)) query lower bound for nonadaptively testing s-sparse polynomials over finite fields of constant size. This shows that in some instances, our general method yields a property tester with query complexity that is optimal (for nonadaptive algorithms) up to a polynomial factor.

Bounded Independence Fools Degree-2 Threshold Functions

For an

Small Approximate Pareto Sets for Bi-objective Shortest Paths and Other Problems

n

Bounding the average sensitivity and noise sensitivity of polynomial threshold functions

-variate degree–

Bounded Independence Fools Halfspaces

2

How good is the Chord algorithm

real polynomial

A Regularity Lemma, and Low-Weight Approximators, for Low-Degree Polynomial Threshold Functions

p

Hardness results for agnostically learning low-degree polynomial threshold functions

, we prove that

Efficiently Testing Sparse GF (2) Polynomials

E_{xsim mathcal{D}}[sgn(p(x))]

Computational Complexity, 2009. CCC '09. 24th Annual IEEE Conference on

is determined up to an additive