Abstract
The spectral representation and classification of Boolean functions have been previously studied and found to be useful in logic design and testing. Spectral techniques also have potential application for reversible and quantum circuits. This paper considers the partitioning of Boolean functions into linear, affine and spectral equivalence classes. A single efficient recursive classification algorithm is presented. It can be used to determine all equivalence classes for small n, and to determine if two functions fall in the same equivalence class for larger n. For two functions in the same equivalence class, the algorithm identifies a sequence of translations to map one to the other.
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Acknowledgements
The authors gratefully acknowledge the constructive comments from the referees of an earlier paper presented at IWSBP2018 which led to improvements in the presentation of this work.
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Miller, D.M., Soeken, M. (2020). An Algorithm for Linear, Affine and Spectral Classification of Boolean Functions. In: Drechsler, R., Soeken, M. (eds) Advanced Boolean Techniques. Springer, Cham. https://doi.org/10.1007/978-3-030-20323-8_9
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DOI: https://doi.org/10.1007/978-3-030-20323-8_9
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