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Abstract <p>In the paper, circuits obtained by superpositions over bases consisting of arbitrary subsets of piecewise-linear functions are studied, and criteria for the expressibility of an arbitrary continuous piecewise-linear function over such bases is proved. Estimates of the linear complexity and nonlinear dependence of the resulting circuits are given.</p>

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A Criterion of Expressibility of CPL Functions in Generalized Bases

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • V. G. Shishlyakov

摘要

Abstract

In the paper, circuits obtained by superpositions over bases consisting of arbitrary subsets of piecewise-linear functions are studied, and criteria for the expressibility of an arbitrary continuous piecewise-linear function over such bases is proved. Estimates of the linear complexity and nonlinear dependence of the resulting circuits are given.