# Function classes and relational constraints stable under compositions with clones

Miguel Couceiro; Stephan Foldes

Discussiones Mathematicae - General Algebra and Applications (2009)

- Volume: 29, Issue: 2, page 109-121
- ISSN: 1509-9415

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topMiguel Couceiro, and Stephan Foldes. "Function classes and relational constraints stable under compositions with clones." Discussiones Mathematicae - General Algebra and Applications 29.2 (2009): 109-121. <http://eudml.org/doc/276920>.

@article{MiguelCouceiro2009,

abstract = {The general Galois theory for functions and relational constraints over arbitrary sets described in the authors' previous paper is refined by imposing algebraic conditions on relations.},

author = {Miguel Couceiro, Stephan Foldes},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {function classes; right (left) composition; Boolean function; invariant relations; relational constraints; composition},

language = {eng},

number = {2},

pages = {109-121},

title = {Function classes and relational constraints stable under compositions with clones},

url = {http://eudml.org/doc/276920},

volume = {29},

year = {2009},

}

TY - JOUR

AU - Miguel Couceiro

AU - Stephan Foldes

TI - Function classes and relational constraints stable under compositions with clones

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2009

VL - 29

IS - 2

SP - 109

EP - 121

AB - The general Galois theory for functions and relational constraints over arbitrary sets described in the authors' previous paper is refined by imposing algebraic conditions on relations.

LA - eng

KW - function classes; right (left) composition; Boolean function; invariant relations; relational constraints; composition

UR - http://eudml.org/doc/276920

ER -

## References

top- [1] M. Couceiro and S. Foldes, Definability of Boolean function classes by linear equations over GF(2), Discrete Applied Mathematics 142 (2004), 29-34. Zbl1051.06009
- [2] M. Couceiro and S. Foldes, On affine constraints satisfied by Boolean functions, Rutcor Research Report 3-2003, Rutgers University, http://rutcor.rutgers.edu/~rrr/.
- [3] M. Couceiro and S. Foldes, On closed sets of relational constraints and classes of functions closed under variable substitutions, Algebra Universalis 54 (2005), 149-165. Zbl1095.08002
- [4] M. Couceiro and S. Foldes, Functional equations, constraints, definability of function classes, and functions of Boolean variables, Acta Cybernetica 18 (2007), 61-75. Zbl1120.06011
- [5] O. Ekin, S. Foldes, P.L. Hammer and L. Hellerstein, Equational characterizations of Boolean function classes, Discrete Mathematics 211 (2000), 27-51. Zbl0947.06008
- [6] S. Foldes and P.L. Hammer, Algebraic and topological closure conditions for classes of pseudo-Boolean functions, Discrete Applied Mathematics 157 (2009), 2818-2827. Zbl1216.06011
- [7] D. Geiger, Closed systems of functions and predicates, Pacific Journal of Mathematics 27 (1968), 95-100. Zbl0186.02502
- [8] L. Lovász, Submodular functions and convexity pp. 235-257 in: Mathematical Programming-The State of the Art, A. Bachem, M. Grötschel, B. Korte (Eds.), Springer, Berlin 1983.
- [9] N. Pippenger, Galois theory for minors of finite functions, Discrete Mathematics 254 (2002), 405-419. Zbl1010.06012
- [10] R. Pöschel, Concrete representation of algebraic structures and a general Galois theory, Contributions to General Algebra, Proceedings Klagenfurt Conference, May 25-28 (1978) 249-272. Verlag J. Heyn, Klagenfurt, Austria 1979.
- [11] R. Pöschel, A general Galois theory for operations and relations and concrete characterization of related algebraic structures, Report R-01/80, Zentralinstitut für Math. und Mech., Berlin 1980. Zbl0435.08001
- [12] R. Pöschel, Galois connections for operations and relations, in Galois connections and applications, K. Denecke, M. Erné, S.L. Wismath (eds.), Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht 2004. Zbl1063.08003
- [13] L. Szabó, Concrete representation of related structures of universal algebras, Acta Sci. Math. (Szeged) 40 (1978), 175-184. Zbl0388.08003

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