Prikladnaya Diskretnaya Matematika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Prikl. Diskr. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Prikladnaya Diskretnaya Matematika, 2016, Number 4(34), Pages 65–73
DOI: https://doi.org/10.17223/20710410/34/5
(Mi pdm564)
 

This article is cited in 10 scientific papers (total in 10 papers)

Mathematical Backgrounds of Computer and Control System Reliability

Lower bounds for lengths of complete diagnostic tests for circuits and inputs of circuits

K. A. Popkov

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
References:
Abstract: Let D1P(n) (D0P(n), D0,1P(n)) be the least length of a complete diagnostic test for the primary inputs of logical circuits implementing Boolean functions in n variables and having constant faults of type 1 (respectively 0, both 0 and 1) on these inputs, DB;1O(n) (DB;0O(n), DB;0,1O(n)) be the least length of a complete diagnostic test for logical circuits consisting of logical gates in a basis B, implementing Boolean functions in n variables, and having constant faults of type 1 (respectively 0, both 0 and 1) on outputs of the logical gates, and B2={x|y}, B2={xy}, B3={x&y,x¯}, B3={xy,x¯}. It is shown that the functions D1P(n), D0P(n), DB2;1O(n), DB2;0O(n), DB3;0,1O(n), DB3;0,1O(n) are not less than 2n/2n42n+(log2n)/2+2 and D0,1P(n) is not less than 2n/2 if n is even, and is not less than 2232n/2 if n is odd.
Keywords: logic circuit, fault, complete diagnostic test, test for inputs of circuits.
Bibliographic databases:
Document Type: Article
UDC: 519.718.7
Language: Russian
Citation: K. A. Popkov, “Lower bounds for lengths of complete diagnostic tests for circuits and inputs of circuits”, Prikl. Diskr. Mat., 2016, no. 4(34), 65–73
Citation in format AMSBIB
\Bibitem{Pop16}
\by K.~A.~Popkov
\paper Lower bounds for lengths of complete diagnostic tests for circuits and inputs of circuits
\jour Prikl. Diskr. Mat.
\yr 2016
\issue 4(34)
\pages 65--73
\mathnet{http://mi.mathnet.ru/pdm564}
\crossref{https://doi.org/10.17223/20710410/34/5}
Linking options:
  • https://www.mathnet.ru/eng/pdm564
  • https://www.mathnet.ru/eng/pdm/y2016/i4/p65
  • This publication is cited in the following 10 articles:
    1. K. A. Popkov, “Short Complete Diagnostic Tests for Circuits Implementing Linear Boolean Functions”, Math. Notes, 113:1 (2023), 80–92  mathnet  crossref  crossref  mathscinet
    2. G. Antyufeev, D. S. Romanov, “On Test Sets Concerning Local Stuck-at Faults of Fixed Multiplicity at the Inputs of Circuits”, Math. Notes, 114:3 (2023), 397–402  mathnet  crossref  crossref  mathscinet
    3. K. A. Popkov, “Short complete diagnostic tests for circuits with two additional inputs in some basis”, Discrete Math. Appl., 33:4 (2023), 219–230  mathnet  crossref  crossref
    4. K. A. Popkov, “Korotkie polnye diagnosticheskie testy dlya skhem s odnim dopolnitelnym vkhodom v standartnom bazise”, PDM, 2022, no. 56, 104–112  mathnet  crossref
    5. K. A. Popkov, “Short conditional complete diagnostic tests for circuits under one-type constant faults of gates”, Discrete Math. Appl., 33:6 (2023), 381–386  mathnet  crossref  crossref
    6. K. A. Popkov, “Short complete diagnostic tests for logic circuits in one infinite basis”, Moscow University Mathematics Bulletin, 77:5 (2022), 250–253  mathnet  crossref  mathscinet  zmath  elib
    7. G. V. Antyufeev, D. S. Romanov, “Tests with Stuck-At and Shift Faults on Circuit Inputs”, Comput Math Model, 31:4 (2020), 494  crossref
    8. K. A. Popkov, “Complete fault detection tests of length 2 for logic networks under stuck-at faults of gates”, J. Appl. Industr. Math., 12:2 (2018), 302–312  mathnet  crossref  crossref  elib
    9. K. A. Popkov, “Short single tests for circuits with arbitrary stuck-at faults at outputs of gates”, Discrete Math. Appl., 29:5 (2019), 321–333  mathnet  crossref  crossref  mathscinet  isi  elib
    10. D. S. Romanov, E. Yu. Romanova, “A method of synthesis of irredundant circuits admitting single fault detection tests of constant length”, Discrete Math. Appl., 29:1 (2019), 35–48  mathnet  crossref  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Прикладная дискретная математика
    Statistics & downloads:
    Abstract page:214
    Full-text PDF :61
    References:49
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025