Abstract : This paper is a contribution to the understanding of the relation between pivotal decompositions of operations on a set A and clones on the same set. In this preliminary study we establish sufficient conditions on a pivotal operation Π so that the corresponding class of Π-decomposable functions constitutes a clone, and discuss the normal form representations that such pivotal operations induce. As a bi-product, we establish that
clones of Π-decomposable functions are determined by the unary sections of their members. We also outline several open questions, providing directions for further research
https://hal.inria.fr/hal-01175698
Contributor : Miguel Couceiro
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Submitted on : Saturday, July 11, 2015 - 6:08:22 PM
Last modification on : Tuesday, December 18, 2018 - 4:38:02 PM
Miguel Couceiro, Bruno Teheux. Clones of pivotally decomposable functions.. 45th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2015), May 2015, Waterloo, Canada. ⟨hal-01175698⟩
