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Expected query complexity of symmetric boolean functions

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3 Author(s)
Acharya, J. ; Univ. of California San Diego, La Jolla, CA, USA ; Jafarpour, A. ; Orlitsky, A.

The problem of finding optimal querying policy, for expected query complexity of symmetric boolean threshold functions was solved in [1] in the context of collocated networks. In this paper, instead of considering the optimal policy to compute the functions, we define the problem of verification of the function value. We use this idea to provide a simpler proof of the optimal querying policy for threshold functions. The method is more generic and is extended to delta and some other symmetric functions. We also provide some partial results for interval functions and finally address a question posed in [1]. Recently we have extended these results to any symmetric function of boolean inputs, which we mention at the end.

Published in:

Communication, Control, and Computing (Allerton), 2011 49th Annual Allerton Conference on

Date of Conference:

28-30 Sept. 2011