Functional equations, constraints, definability of function classes, and functions of Boolean variables

Couceiro, Miguel and Foldes, Stephan: Functional equations, constraints, definability of function classes, and functions of Boolean variables. In: Acta cybernetica, (18) 1. pp. 61-75. (2007)

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Abstract

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.

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 2007
Volume: 18
Number: 1
ISSN: 0324-721X
Page Range: pp. 61-75
Language: angol
Event Title: Kalmár Workshop on Logic in Computer Science, 2003, Szeged
Uncontrolled Keywords: Természettudomány, Informatika
Additional Information: Bibliogr.: p. 74-75.; Abstract
Date Deposited: 2016. Oct. 15. 12:25
Last Modified: 2018. Jun. 05. 13:54
URI: http://acta.bibl.u-szeged.hu/id/eprint/12804

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