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: | English |
| Place of Publication: | Szeged |
| Event Title: | Kalmár Workshop on Logic in Computer Science (2003) (Szeged) |
| Related URLs: | http://acta.bibl.u-szeged.hu/38523/ |
| Uncontrolled Keywords: | Számítástechnika, Kibernetika |
| Additional Information: | Bibliogr.: p. 74-75. ; összefoglalás angol nyelven |
| Subjects: | 01. Natural sciences 01. Natural sciences > 01.02. Computer and information sciences |
| Date Deposited: | 2016. Oct. 15. 12:25 |
| Last Modified: | 2022. Jun. 16. 11:04 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/12804 |
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