Clausal relations and C-clones

Edith Vargas

Discussiones Mathematicae - General Algebra and Applications (2010)

  • Volume: 30, Issue: 2, page 147-171
  • ISSN: 1509-9415

Abstract

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We introduce a special set of relations called clausal relations. We study a Galois connection Pol-CInv between the set of all finitary operations on a finite set D and the set of clausal relations, which is a restricted version of the Galois connection Pol-Inv. We define C-clones as the Galois closed sets of operations with respect to Pol-CInv and describe the lattice of all C-clones for the Boolean case D = {0,1}. Finally we prove certain results about C-clones over a larger set.

How to cite

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Edith Vargas. "Clausal relations and C-clones." Discussiones Mathematicae - General Algebra and Applications 30.2 (2010): 147-171. <http://eudml.org/doc/276531>.

@article{EdithVargas2010,
abstract = {We introduce a special set of relations called clausal relations. We study a Galois connection Pol-CInv between the set of all finitary operations on a finite set D and the set of clausal relations, which is a restricted version of the Galois connection Pol-Inv. We define C-clones as the Galois closed sets of operations with respect to Pol-CInv and describe the lattice of all C-clones for the Boolean case D = \{0,1\}. Finally we prove certain results about C-clones over a larger set.},
author = {Edith Vargas},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {clone; Galois connection; clausal relation; C-clone; clausal relations},
language = {eng},
number = {2},
pages = {147-171},
title = {Clausal relations and C-clones},
url = {http://eudml.org/doc/276531},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Edith Vargas
TI - Clausal relations and C-clones
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2010
VL - 30
IS - 2
SP - 147
EP - 171
AB - We introduce a special set of relations called clausal relations. We study a Galois connection Pol-CInv between the set of all finitary operations on a finite set D and the set of clausal relations, which is a restricted version of the Galois connection Pol-Inv. We define C-clones as the Galois closed sets of operations with respect to Pol-CInv and describe the lattice of all C-clones for the Boolean case D = {0,1}. Finally we prove certain results about C-clones over a larger set.
LA - eng
KW - clone; Galois connection; clausal relation; C-clone; clausal relations
UR - http://eudml.org/doc/276531
ER -

References

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  1. [1] N. Creignou, M. Hermann, A. Krokhin and G. Salzer, Complexity of clausal constraints over chains, Theory Comput. Syst., Theory of Computing Systems 42 (2) (2008), 239-255. doi: 10.1007/s00224-007-9003-z Zbl1141.68034
  2. [2] E.L. Post, The Two- Valued Iterative Systems of Mathematical Logic, Annals of Mathematics Studies, no. 5, Princeton University Press, Princeton, N. J. (1941), pages viii+122. Zbl0063.06326
  3. [3] R. Pöschel and L.A. Kalužnin, Funktionen- und Relationenalgebren, Mathematische Monographien [Mathematical Monographs], 15, VEB Deutscher Verlag der Wissenschaften, Berlin (1979), pages 259 

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