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Local Correction of Juntas (1109.3639v2)

Published 16 Sep 2011 in cs.CC, cs.IT, and math.IT

Abstract: A Boolean function f over n variables is said to be q-locally correctable if, given a black-box access to a function g which is "close" to an isomorphism f_sigma of f, we can compute f_sigma(x) for any x in Z_2n with good probability using q queries to g. We observe that any k-junta, that is, any function which depends only on k of its input variables, is O(2k)-locally correctable. Moreover, we show that there are examples where this is essentially best possible, and locally correcting some k-juntas requires a number of queries which is exponential in k. These examples, however, are far from being typical, and indeed we prove that for almost every k-junta, O(k log k) queries suffice.

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