We introduce weakenings of two of the more prominent open problems in the classification of C∗-algebras, namely the quasidiagonality problem and the UCT problem. We show that the a positive solution of the conjunction of the two weaker problems implies a positive solution of the original quasidiagonality problem as well as allows us to give a local, finitary criteria for the MF problem, which a...

In this paper we consider the problem of deciding membership in Dyck languages, a fundamental family of context-free languages, comprised of well-balanced strings of parentheses. In this problem we are given a string of length n in the alphabet of parentheses of m types and must decide if it is well-balanced. We consider this problem in the property testing setting, where one would like to make...

We study lower bounds for testing membership in families of linear/affine-invariant Boolean functions over the hypercube. A family of functions P ⊆ {{0, 1} → {0, 1}} is linear/affine invariant if for any f ∈ P , it is the case that f ◦L ∈ P for any linear/affine transformation L of the domain. Motivated by the recent resurgence of attention to the permutation isomorphism problem, we first focus...

In this paper we give the first deterministic polynomial time algorithm for testing whether a diagonal depth-3 circuit C(x1, . . . , xn) (i.e. C is a sum of powers of linear functions) is zero. We also prove an exponential lower bound showing that such a circuit will compute determinant or permanent only if there are exponentially many linear functions. Our techniques generalize to the followin...

Karl Svozil† Institut für Theoretische Physik, University of Technology Vienna, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria Abstract Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as criteria for the v...

A sequence f : {1, . . . , n} → R contains a permutation π of length k if there exist i1 < . . . < ik such that f(ix) < f(iy) iff π(x) < π(y); otherwise, f is said to be π-free. As a simple special case, f is weakly monotone increasing iff it is (2, 1)-free. The problem of (one-sided) testing π-freeness in a sequence (or equivalently, efficiently finding a π-copy in a sequence far from π-freene...

Recall that we showed that there is an algorithm for testing triangle-freeness of dense graphs that had a dependence on 1/ that was quite high. While we cannot exactly match that dependence with a lower bound, we’ll show that a super-polynomial dependence is necessary. Here we’ll give the proof only for the one-sided error case, and note that it can be extended to two-sided error algorithms. Na...

We present upper bounds on the size of codes that are locally testable by querying only two input symbols. For linear codes, we show that any 2-locally testable code with minimal distance δn over any finite field F cannot have more than |F| codewords. This result holds even for testers with two-sided error. For general (non-linear) codes we obtain the exact same bounds on the code size as a fun...

In this paper, we consider several property testing problems and ask how the query complexity depends on the distance parameter ǫ. We achieve new lower bounds in this setting for the problems of testing whether a function is monotone and testing whether the function has low Fourier degree. For monotonicity testing, our lower bound matches the recent upper bound of Chakrabarty and Seshadhri [12].