Abstract
The paper presents conditions of extension of the weakly defined Boolean functions to their full affine form. The main goal of the analysis is a fast estimation whether a given incompletely defined function can be extended to a full affine form. If it is possible a simple algorithm of the states completion has been proposed. In such a case undefined points are clearly replaced by 0, 1 values. Spectral coefficients of a Boolean function allow to determine whether a partially defined function can be realised as affine.
Keywords
MSC
06E30, 94C10, 43A32
Cite this article
@article{cai-1882,
author = {Piotr Porwik},
title = {Conditions of the Affine Extension of an Incompletely Defined Boolean Function},
journal = {Computing and Informatics},
volume = {29},
number = {6+},
pages = {1073--1088},
year = {2010},
issn = {1335-9150},
url = {https://cai.type.sk/content/2010/6%2B/conditions-of-the-affine-extension-of-an-incompletely-defined-boolean-function/}
}
TY - JOUR AU - Piotr Porwik TI - Conditions of the Affine Extension of an Incompletely Defined Boolean Function JO - Computing and Informatics VL - 29 IS - 6+ SP - 1073 EP - 1088 PY - 2010 SN - 1335-9150 UR - https://cai.type.sk/content/2010/6%2B/conditions-of-the-affine-extension-of-an-incompletely-defined-boolean-function/ KW - Walsh coefficients KW - coefficients distribution KW - incompletely defined Boolean function KW - affine function ER -
Porwik, P. (2010). Conditions of the Affine Extension of an Incompletely Defined Boolean Function. Computing and Informatics, 29(6+), 1073–1088. https://cai.type.sk/content/2010/6%2B/conditions-of-the-affine-extension-of-an-incompletely-defined-boolean-function/