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Boolean Functions: Degree and Support

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Abstract

In this paper we establish some properties about Boolean functions that allow us to relate their degree and their support. These properties allow us to compute the degree of a Boolean function without having to calculate its algebraic normal form. Furthermore, we introduce some linear algebra properties that allow us to obtain the degree of a Boolean function from the dimension of a linear or affine subspace. Finally we derive some algorithms and compute the average time to obtain the degree of some Boolean functions from its support.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat d’Alacant, Carretera de Sant Vicent del Raspeig, s/n, 03690, Sant Vicent del Raspeig, Alacant, Spain

    Joan-Josep Climent & Verónica Requena

  2. Departament de Fonaments de l’Anàlisi Econòmica, Universitat d’Alacant, Carretera de Sant Vicent del Raspeig, s/n, 03690, Sant Vicent del Raspeig, Alacant, Spain

    Francisco J. García

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  1. Joan-Josep Climent
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  2. Francisco J. García
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  3. Verónica Requena
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Correspondence to Joan-Josep Climent.

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Climent, JJ., García, F.J. & Requena, V. Boolean Functions: Degree and Support. Math.Comput.Sci. 12, 349–369 (2018). https://doi.org/10.1007/s11786-018-0350-8

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  • DOI: https://doi.org/10.1007/s11786-018-0350-8

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