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On generalized boolean functions III. the case A={ 0,1 } by Nicolae Ţăndăreanu is a Computer Science article available to read on EtoBox.

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In this paper we give some properties of (0, 1}-generalized Boolean functions. The main restit is the following: by composition of the Boolean functions of n variables with th.e elements of GBFJO, l] we obtain all the (0, I}-generalized Boolean functions of n variables. Suppose J3 is a Boolean algebra which does not reduce to the algebra (0, 1). We denote by U, 0, -, + disjunction, conjunction, negation and sum ring, respectively [2]. Let A be a finite set such that (0,l) s A c B, where c denotes the proper inclusion. The concept of generalized Boolean function is based on the following idea: instead of xa in canonical disjunctive form of a Boolean function, where Q ~40, l}, we introduce the value of a function which verifies some properties, similar to negation. More precisely, we denote by G(A, B) the set of those functions g : A Y I3 --, B for which g(Q, 0) = g(l, 1) and By GB&[A] we denote the set of those functions f : B" + B for which there is g E G(A, B) such that

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Author

Nicolae Ţăndăreanu

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0012-365X)

Published

1984

Language

EN

Field

Computer Science (Physical Sciences)