This article is cited in 3 papers

Theoretical Foundations of Applied Discrete Mathematics

On linear decomposition of Boolean functions

A. V. Cheremushkin

EMA IS, Moscow, Russia

Abstract: Disjunctive decompositions of Boolean functions taken after a linear substitution on the set of arguments are considered. For any component of such a decomposition, a notion of a substantial variables subspace is introduced. The main topic of the article is to give some sufficient condition under which the both these subspaces unequally determine each other in a simple disjunctive decomposition of a function having the trivial stabiliser group of shifts. The case of iterative disjunctive decomposition is considered too.

Keywords: Boolean function, vector space, dual space, simple disjunctive decomposition, iterative disjunctive decomposition.

UDC: 519.719.325

DOI: 10.17223/20710410/31/4

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