On equational definability of function classes
Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás
Proceedings of the 41st IEEE International Symposium on Multiple-Valued Logic (ISMVL 2011), IEEE Computer Society, Los Alamitos, (2011), 182-186
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 a class of functions to be definable by such equations, and show that for certain choices of clones these conditions are also sufficient.