Pravesh Kothari

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This paper presents a randomized scheduler for finding concurrency bugs. Like current stress-testing methods, it repeatedly runs a given test program with supplied inputs. However, it improves on stress-testing by finding buggy schedules more effectively and by quantifying the probability of missing concurrency bugs. Key to its design is the(More)
Owing to several applications in large scale learning and vision problems, fast submodular function minimization (SFM) has become a critical problem. Theoretically, unconstrained SFM can be performed in polynomial time [10, 11]. However, these algorithms are typically not practical. In 1976, Wolfe [21] proposed an algorithm to find the minimum Euclidean(More)
We show that all non-negative submodular functions have high noise-stability. As a consequence, we obtain a polynomial-time learning algorithm for this class with respect to any product distribution on {−1, 1} (for any constant accuracy parameter ). Our algorithm also succeeds in the agnostic setting. Previous work on learning submodular functions required(More)
Fortnow and Klivans proved the following relationship between efficient learning algorithms and circuit lower bounds: if a class C ⊆ P/poly of Boolean circuits is exactly learnable with membership and equivalence queries in polynomial-time, then EXP * C (the class EXP was subsequently improved to EXP by Hitchcock and Harkins). In this paper, we improve on(More)
We study the complexity of approximate representation and learning of submodular functions over the uniform distribution on the Boolean hypercube {0, 1}. Our main result is the following structural theorem: any submodular function is -close in `2 to a real-valued decision tree (DT) of depth O(1/ ). This immediately implies that any submodular function is(More)
We study the problem of approximating and learning coverage functions. A function c : 2 → R is a coverage function, if there exists a universe U with non-negative weights w(u) for each u ∈ U and subsets A1, A2, . . . , An of U such that c(S) = ∑ u∈∪i∈SAi w(u). Alternatively, coverage functions can be described as non-negative linear combinations of monotone(More)
Let <i>P</i>:{0,1}<sup><i>k</i></sup> &#226;†’ {0,1} be a nontrivial <i>k</i>-ary predicate. Consider a random instance of the constraint satisfaction problem (<i>P</i>) on <i>n</i> variables with &#206;” <i>n</i> constraints, each being <i>P</i> applied to <i>k</i> randomly chosen literals. Provided the constraint density satisfies &#206;” &#226;‰« 1, such(More)