@article{Couceiro_Foldes_2007, title={Functional equations, constraints, definability of function classes, and functions of Boolean variables}, volume={18}, url={https://cyber.bibl.u-szeged.hu/index.php/actcybern/article/view/3706}, abstractNote={The paper deals with classes of functions of several variables defined on an arbitrary set A and taking values in a possibly different set B. Definability of function classes by functional equations is shown to be equivalent to definability by relational constraints, generalizing a fact established by Pippenger in the case A = B = {0,1}. Conditions for a class of functions to be definable by constraints of a particular type are given in terms of stability under certain functional compositions. This leads to a correspondence between functional equations with particular algebraic syntax and relational constraints with certain invariance properties with respect to clones of operations on a given set. When A = {0,1} and B is a commutative ring, such B-valued functions of n variables are represented by multilinear polynomials in n indeterminates in B[X1,..., Xn], Functional equations are given to describe classes of field-valued functions of a specified bounded degree. Classes of Boolean and pseudo-Boolean functions are covered as particular cases.}, number={1}, journal={Acta Cybernetica}, author={Couceiro, Miguel and Foldes, Stephan}, year={2007}, month={Jan.}, pages={61-75} }