On the Spectral Properties of Symmetric FunctionsReport as inadecuate

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1 CMU - Carnegie Mellon University Pittsburgh 2 LIP - Laboratoire de l-Informatique du Parallélisme 3 Chennai Mathematical Institute Inde

Abstract : We characterize the approximate monomial complexity, sign monomial complexity , and the approximate L 1 norm of symmetric functions in terms of simple combinatorial measures of the functions. Our characterization of the approximate L 1 norm solves the main conjecture in AFH12. As an application of the characterization of the sign monomial complexity, we prove a conjecture in ZS09 and provide a characterization for the unbounded-error communication complexity of symmetric-xor functions.

Author: Anil Ada - Omar Fawzi - Raghav Kulkarni -

Source: https://hal.archives-ouvertes.fr/


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