PittsburghV1, France, Analysis, bibRecord, 000017

On the Spectral Properties of Symmetric Functions

Identifieur interne : 000017 ( France/Analysis ); précédent : 000016; suivant : 000018

On the Spectral Properties of Symmetric Functions

Auteurs : Anil Ada [États-Unis] ; Omar Fawzi [France] ; Raghav Kulkarni [Inde]

Source :

RBID : Hal:hal-01505075

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.

Url:

https://hal.archives-ouvertes.fr/hal-01505075

Affiliations:

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Hal:hal-01505075

Le document en format XML

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<front><div type="abstract" xml:lang="en">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.</div>
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On the Spectral Properties of Symmetric Functions

On the Spectral Properties of Symmetric Functions

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Abstract

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