On equational definability of function classes

J. Mult.-Valued Logic Soft Comput., 24 (2015), 203–222
http://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-24-number-1-4-2015/mvlsc-24-1-4-p-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.