Authors: Stanković, Radomir 
Astola, Jaakko
Moraga, Claudio
Title: Convolution on finite groups and fixed-polarity polynomial expressions
Journal: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume: 5717 LNCS
First page: 501
Last page: 509
Conference: 12th International Conference on Computer Aided Systems Theory, EUROCAST 2009; Las Palmas de Gran Canaria; Spain; 15 February 2009 through 20 February 2009
Issue Date: 1-Dec-2009
Rank: M23
ISBN: 978-3-642-04771-8
ISSN: 0302-9743
DOI: 10.1007/978-3-642-04772-5_65
This paper discusses relationships among convolution matrices and fixed-polarity matrices for polynomial expressions of discrete functions on finite groups. Switching and multiple-valued functions are considered as particular examples of discrete functions on finite groups. It is shown that if the negative literals for variables are defined in terms of the shift operators on domain groups, then there is a relationship between the polarity matrices and convolution matrices. Therefore, the recursive structure of polarity matrices follows from the recursive structure of convolution matrices. This structure is determined by the assumed decomposition of the domain groups for the considered functions.
Keywords: Convolution | Finite groups | Polynomial expressions | Spectral representations
Publisher: Springer Link

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