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On equational definability of function classes

Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás

J. Mult.-Valued Logic Soft Comput., 24 (2015), 203–222

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.