On equational definability of function classes

Miguel Couceiro (1) , Erkko Lehtonen (2) , Tamas Waldhauser (3)

1 ORPAILLEUR - Knowledge representation, reasonning
2 Centro de Algebra da Universidade de Lisboa
3 University of Szeged [Szeged]

We propose a notion of functional equation for functions of a fixed arity, which is based on a pair of clones. We present necessary conditions for aclass of functions to be definable by such equations, and show that for certain choices of clones these conditions are also sufficient.

Domaines: Mathématiques [math]

Miguel Couceiro, Erkko Lehtonen, Tamas Waldhauser. On equational definability of function classes. Journal of Multiple-Valued Logic and Soft Computing, 2015, 24 (1–4), pp.203-222. ⟨hal-01093668⟩