Overlaps help: Improved bounds for group testing with interval queries

Improved Bounds for Testing Juntas

We consider the problem of testing functions for the property of being a k-junta (i.e., of depending on at most k variables). Fischer, Kindler, Ron, Safra, and Samorodnitsky (J. Comput. Sys. Sci., 2004 ) showed that Õ(k)/ queries are sufficient to test k-juntas, and conjectured that this bound is optimal for non-adaptive testing algorithms. Our main result is a non-adaptive algorithm for testin...

Improved Interval Bounds for Ranges of Functions

Optimal Group Testing Strategies with Interval Queries and Their Application to Splice Site Detection

We consider the following constrained version of the classical Group Testing Problem: Given a finite set of items identified with the set of natural numbers {1, 2, . . . , n} and an unknown distinguished subset P ⊆ {1, 2, . . . , n} of up to p positive elements, the goal is to identify the items in P by asking the least number of queries of the type “does the subset Q ⊆ {1, 2, . . . , n} inters...

Improved bounds for testing Dyck languages

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...

Improved Bounds for Testing Forbidden Order Patterns

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...