Functional equations, constraints, definability of function classes, and functions of Boolean variables
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...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2007
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| Sorozat: | Acta cybernetica
18 No. 1 |
| Kulcsszavak: | Számítástechnika, Kibernetika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/12804 |
| LEADER | 01963nab a2200241 i 4500 | ||
|---|---|---|---|
| 001 | acta12804 | ||
| 005 | 20220616110408.0 | ||
| 008 | 161015s2007 hu o 0|| eng d | ||
| 022 | |a 0324-721X | ||
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Couceiro Miguel | |
| 245 | 1 | 0 | |a Functional equations, constraints, definability of function classes, and functions of Boolean variables |h [elektronikus dokumentum] / |c Couceiro Miguel |
| 260 | |c 2007 | ||
| 300 | |a 61-75 | ||
| 490 | 0 | |a Acta cybernetica |v 18 No. 1 | |
| 520 | 3 | |a 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. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Számítás- és információtudomány | |
| 695 | |a Számítástechnika, Kibernetika | ||
| 700 | 0 | 1 | |a Foldes Stephan |e aut |
| 710 | |a Kalmár Workshop on Logic in Computer Science (2003) (Szeged) | ||
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/12804/1/Couceiro_2007_ActaCybernetica.pdf |z Dokumentum-elérés |