Abstract

The paper is focused on decomposition of Boolean functions in the form \(f_{1}\circ\ldots\circ f_{m}\), where \(\circ\) is a commutative associative operation and \(f_{1},\ldots,f_{m}\) are Boolean functions with fewer arguments. For each commutative associative operation, we determine the necessary and sufficient conditions of the absence of such a decomposition and find the related complexity class.

中文翻译：

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布尔函数关于可交换联想运算的不可约性

摘要

本文着重于分解形式为\（f_ {1} \ circ \ ldots \ circ f_ {m} \）的布尔函数，其中\（\ circ \）是可交换的关联运算，\（f_ {1} ，\ ldots，f_ {m} \）是带有较少参数的布尔函数。对于每个可交换的关联运算，我们确定不存在这种分解的必要条件和充分条件，并找到相关的复杂度类别。