A Stateful Implementation of a Random Function Supporting Parity Queries over Hypercubes

Abstract. Motivated by an open problem recently suggested by Goldreich et al., we study truthful implementations of a random binary function supporting compound XOR queries over sub-cubes of the hypercube {0, 1}n . We introduce a relaxed model of an implementation, which we call a stateful implementation, and show how to implement the desired specification in this model. The main technical construction is an algorithm for detecting linear dependencies between n dimensional hypercubes, viewed as characteristic vectors in F {0,1}n 2 . Using coding theoretic techniques, we first exhibit a randomized algorithm for detecting such dependencies. We then show how a recent approach by Raz and Shpilka for polynomial identity testing in non-commutative models of computation can be applied to obtain a deterministic algorithm.

• Type: Conference
• Year: 2004
• Where: APPROX
• Authors: Andrej Bogdanov, Hoeteck Wee
• Keywords: Algorithms, APPROX 2004, Compound Xor Queries, Goldreich Et Al, Randomized Algorithm