Monotonicity Tester for Boolean Functions over the Hypergrid
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چکیده
We study monotonicity testing of Boolean functions over the hypergrid [n] and design a nonadaptive tester with 1-sided error whose query complexity is Õ(d) ·poly(log n, 1/ε). Previous to our work, the best known testers had query complexity linear in d but independent of n. We improve upon these testers as long as n = 2 o(1) . To obtain our results, we work with what we call the augmented hypergrid, which adds extra edges to the hypergrid. Our main technical contribution is a Margulis-style isoperimetric result for the augmented hypergrid, and our tester, like previous testers for the hypercube domain, performs directed random walks on this structure. ∗Department of Computer Science, University of California, Santa Cruz. Email: [email protected]. †Department of Computer Science, Dartmouth College. Email: [email protected]. ‡Department of Computer Science, University of California, Santa Cruz. Email: [email protected]. ISSN 1433-8092 Electronic Colloquium on Computational Complexity, Report No. 159 (2017)
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تاریخ انتشار 2017