# Clausal relations and C-clones

Discussiones Mathematicae - General Algebra and Applications (2010)

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

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topEdith 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

top- [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] 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] 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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