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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1153, author = {Miguel Couceiro and Stephan Foldes}, title = {Function classes and relational constraints stable under compositions with clones}, journal = {Discussiones Mathematicae - General Algebra and Applications}, volume = {29}, year = {2009}, pages = {109-121}, zbl = {1203.06005}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1153} }
Miguel Couceiro; Stephan Foldes. Function classes and relational constraints stable under compositions with clones. Discussiones Mathematicae - General Algebra and Applications, Tome 29 (2009) pp. 109-121. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1153/
[000] [1] M. Couceiro and S. Foldes, Definability of Boolean function classes by linear equations over GF(2), Discrete Applied Mathematics 142 (2004), 29-34. | Zbl 1051.06009
[001] [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/.
[002] [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. | Zbl 1095.08002
[003] [4] M. Couceiro and S. Foldes, Functional equations, constraints, definability of function classes, and functions of Boolean variables, Acta Cybernetica 18 (2007), 61-75. | Zbl 1120.06011
[004] [5] O. Ekin, S. Foldes, P.L. Hammer and L. Hellerstein, Equational characterizations of Boolean function classes, Discrete Mathematics 211 (2000), 27-51. | Zbl 0947.06008
[005] [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. | Zbl 1216.06011
[006] [7] D. Geiger, Closed systems of functions and predicates, Pacific Journal of Mathematics 27 (1968), 95-100. | Zbl 0186.02502
[007] [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.
[008] [9] N. Pippenger, Galois theory for minors of finite functions, Discrete Mathematics 254 (2002), 405-419. | Zbl 1010.06012
[009] [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.
[010] [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. | Zbl 0435.08001
[011] [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. | Zbl 1063.08003
[012] [13] L. Szabó, Concrete representation of related structures of universal algebras, Acta Sci. Math. (Szeged) 40 (1978), 175-184. | Zbl 0388.08003