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On generalized Boolean functions II

Authors
Journal
Discrete Mathematics
0012-365X
Publisher
Elsevier
Publication Date
Volume
40
Identifiers
DOI: 10.1016/0012-365x(82)90127-3

Abstract

Abstract This cycle of papers is based on the concept of generalized Bolean functions introduced by the author in the first article of the series. Every generalized Boolean function f: B n → B can be written in a manner similar to the canonical disjunctive form using some function defined on A× B, where A is a finite subset of B containing 0 and 1. The set of those functions f is denoted by GBF n [ A]. In this paper the following questions are presented: (1) What is the relationship between GBF n [ A 1] and GBF n [ A 2] when A 1⊂ A 2. (2) What can be said about GBF n [ A 1∩ A 2] and GBF n [ A 1∪ A 2] in comparison with GBF n [ A 1]∩GBF n [ A 2] and GBF n [ A 1]∪GBF n [ A 2], respectively.

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