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Autosymmetric and Dimension Reducible Multiple-Valued Functions
Anna Bernasconi and Valentina Ciriani

Autosymmetric and dimension reducible functions are classes of Boolean functions whose regular structure can be exploited by synthesis algorithms in order to reduce the minimization time and to derive more compact algebraic forms. In this paper we first propose a generalization of these classes of functions to the multiple-valued logic framework. Then we study their spectral properties and provide a complete spectral characterization for both the Boolean and the multiple-valued setting. We finally show that the two types of structural regularity are one the “spectral counterpart” of the other.

Keywords: Multiple-valued logic synthesis; functions regularities; affine spaces; autosymmetric functions; dimension reducible functions; spectral transform

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