[en] This paper is a contribution to the understanding of the relation between pivotal decompositions of operations on a set and clones on the same set.
Disciplines :
Mathématiques
Auteur, co-auteur :
Couceiro, Miguel; CNRS - Inria Nancy Grand Est - Université de Lorraine
TEHEUX, Bruno ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Clones of Pivotally Decomposable Functions
Date de publication/diffusion :
20 mai 2015
Nom de la manifestation :
ISMVL 2015 (IEEE International Symposium on Multiple-Valued Logic)
Lieu de la manifestation :
Waterloo, Canada
Date de la manifestation :
from May 18 2015 to May 20 2015
Manifestation à portée :
International
Titre de l'ouvrage principal :
Multiple-Valued Logic (ISMVL), 2015 IEEE International Symposium on
R.E. Barlow, F. Proschan. Importance of system components and fault tree events, Stochastic Process. Appl. 3 (1975) 153-172.
M. Couceiro, S. Foldes, E. Lehtonen. Composition of Post classes and normal forms of Boolean functions, Discrete Math. 306 (2006) 3223-3243.
M. Couceiro, E. Lehtonen, J.-L. Marichal, T. Waldhauser. An algorithm for producing median normal form representations for Boolean functions, in the proceedings of the Reed-Muller Workshop 2011, 49-54, 2011.
M. Couceiro, J.-L. Marichal. Polynomial functions over bounded distributive lattices, J. Multiple-Valued Logic Soft Comput. 18 (2012) 247-256.
M. Couceiro, M. Pouzet. On a quasi-order on Boolean functions, Theoret. Comput. Sci. 396 (2008) 71-87.
K. Denecke, S. L. Wismath. Universal Algebra and Applications in Theoretical Computer Science, Chapman & Hall/CRC, Boca Raton, 2002.
L. Hellerstein. On generalized constraints and certificates, Discrete Math. 226 (2001) 211-232.
D. Lau. Function Algebras on Finite Sets, Springer-Verlag, Berlin, Heidelberg, 2006.
E. Lehtonen. Descending chains and antichains of the unary, linear, monotone subfunction relations, Order 23 (2006) 129-142.
E. Lehtonen, Á . Szendrei. Equivalence of operations with respect to discriminator clones, Discrete Math. 309 (2009) 673-685.
J.-L. Marichal, B. Teheux. Pivotal decompositions of functions, Discrete Appl. Math., 174:102-112, 2014.
F. Miyata. Realization of arbitrary logical functions using majority elements, IEEE Trans. on Electronic Computers EC-12 (1963) 183-191.
N. Pippenger. Galois theory for minors of finite functions, Discrete Math. 254 (2002) 405-419.
E. L. Post. The Two-Valued Iterative Systems of Mathematical Logic, Annals of Mathematical Studies, vol. 5, Princeton University Press, Princeton, 1941.
C.E. Shannon. A symbolic analysis of relay and switching circuits, Trans. Am. Inst. Electr. Eng. 57 (1938) 713-723.
Y. Tohma. Decompositions of logical functions using majority decision elements, IEEE Trans. on Electronic Computers EC-13 (1964) 698-705.
