Function classes and relational constraints stable under compositions with clones

• Autorzy: Miguel Couceiro , Stephan Foldes
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 06E30: Boolean functions

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2009
• Tom: 29
• Numer: 2
• Strony: 109-121

Daty

wydano

2009

otrzymano

2009-04-23

poprawiono

2009-07-01

Twórcy

autor

Miguel Couceiro

• University of Luxembourg, Mathematics Research Unit, 6, rue Richard Coudenhove-Kalergi L-1359 Luxembourg, G.-D. Luxembourg

autor

Stephan Foldes

• Institute of Mathematics, Tampere University of Technology, PL553, 33101 Tampere, Finland

Bibliografia

• [1] M. Couceiro and S. Foldes, Definability of Boolean function classes by linear equations over GF(2), Discrete Applied Mathematics 142 (2004), 29-34.
• [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.
• [4] M. Couceiro and S. Foldes, Functional equations, constraints, definability of function classes, and functions of Boolean variables, Acta Cybernetica 18 (2007), 61-75.
• [5] O. Ekin, S. Foldes, P.L. Hammer and L. Hellerstein, Equational characterizations of Boolean function classes, Discrete Mathematics 211 (2000), 27-51.
• [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.
• [7] D. Geiger, Closed systems of functions and predicates, Pacific Journal of Mathematics 27 (1968), 95-100.
• [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.
• [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.
• [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.
• [13] L. Szabó, Concrete representation of related structures of universal algebras, Acta Sci. Math. (Szeged) 40 (1978), 175-184.

Identyfikatory

DOI

10.7151/dmgaa.1153