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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

Abstract

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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.

How to cite

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Miguel 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

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  1. [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. [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. [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. [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. [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. [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. [7] D. Geiger, Closed systems of functions and predicates, Pacific Journal of Mathematics 27 (1968), 95-100. Zbl0186.02502
  8. [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. [9] N. Pippenger, Galois theory for minors of finite functions, Discrete Mathematics 254 (2002), 405-419. Zbl1010.06012
  10. [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. [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. [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. [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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