Year: 2020
Type: preprint
Abstract: The M{ö}bius transform is a crucial transformation into the Boolean world; it allows to change the Boolean representation between the True Table and Algebraic Normal Form. In this work, we introduce a new algebraic point of view of this transformation based on the polynomial form of Boolean functions. It appears that we can perform a new notion: the M{ö}bius computation variable by variable and new computation properties. As a consequence, we propose new algorithms which can produce a huge speed up of the M{ö}bius computation for sub-families of Boolean function. Furthermore we compute directly the M{ö}bius transformation of some particular Boolean functions. Finally, we show that for some of them the Hamming weight is directly related to the algebraic degree of specific factors.
Source: arXiv (Cornell University)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3018156573