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Abstract <p> The problem of implementing Boolean functions by irredundant Boolean circuits in the Zhegalkin basis which admit short single-fault tests in the presence of arbitrary stuck-at faults at gate outputs is considered. It is proved that the Shannon function of the length of a single-fault fault detection (single-fault diagnostic) test does not exceed <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3087_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(3\)</EquationSource> </InlineEquation> (respectively, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3087_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(5\)</EquationSource> </InlineEquation>). </p>

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Short Single-Fault Tests for Circuits in the Zhegalkin Basis with Arbitrary Stuck-At Faults of Gates

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • K. A. Popkov

摘要

Abstract

The problem of implementing Boolean functions by irredundant Boolean circuits in the Zhegalkin basis which admit short single-fault tests in the presence of arbitrary stuck-at faults at gate outputs is considered. It is proved that the Shannon function of the length of a single-fault fault detection (single-fault diagnostic) test does not exceed \(3\) (respectively, \(5\) ).