Single fault detection tests for generalized iterative switching circuits

Abstract The following results are proved: any nonconstant Boolean function may be implemented by an irredundant circuit of gates in the basis {x& y, x, x ⊕ y ⊕ z} admitting a single fault detection test of length at most 2 with respect to arbitrary stuck-at faults at outputs of gates, there exists a six-place Boolean function ψ such that any nonconstant Boolean function may be implemented by an irredundant circuit of gates in the basis {ψ} admitting a single diagnostic test of length at most 3 with respect to arbitrary stuck-at faults at outputs of gates.

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A method of synthesis of irredundant circuits admitting single fault detection tests of constant length

Discrete Mathematics and Applications ◽

10.1515/dma-2019-0005 ◽

2019 ◽

Vol 29 (1) ◽

pp. 35-48

Author(s):

Dmitry S. Romanov ◽

Elena Yu. Romanova

Keyword(s):

Fault Detection ◽

Boolean Function ◽

Constructive Proof ◽

List Type ◽

Combinational Circuit ◽

Constant Length ◽

Single Fault ◽

Inputs And Outputs

Abstract A constructive proof is given that in each of the bases B′ = {x&y, x⊕y, x ∼ y}, B1 = {x&y, x⊕y, 1} any n-place Boolean function may be implemented: by an irredundant combinational circuit with n inputs and one output admitting (under single stuck-at faults at inputs and outputs of gates) a single fault detection test of length at most 16, by an irredundant combinational circuit with n inputs and one output admitting (under single stuck-at faults at inputs and outputs of gates and at primary inputs) a single fault detection test of length at most 2n−2log2 n+O(1); besides, there exists an n-place function that cannot be implemented by an irredundant circuit admitting a detecting test whose length is smaller than 2n−2log2 n − Ω(1), by an irredundant combinational circuit with n inputs and three outputs admitting (under single stuck-at faults at inputs and outputs of gates and at primary inputs) a single fault detection test of length at most 17.

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A method for synthesis of easily-testable circuits in some basis admitting single fault detection tests of constant length

Moscow University Mathematics Bulletin ◽

10.3103/s0027132212020064 ◽

2012 ◽

Vol 67 (2) ◽

pp. 69-73

Author(s):

D. S. Romanov

Keyword(s):

Fault Detection ◽

Constant Length ◽

Single Fault

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A note on single fault detection in positive resistor circuits

IEEE Transactions on Circuits and Systems ◽

10.1109/tcs.1978.1084385 ◽

1978 ◽

Vol 25 (1) ◽

pp. 46-48 ◽

Cited By ~ 10

Author(s):

T. Trick ◽

R. Chien

Keyword(s):

Fault Detection ◽

Single Fault

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Constant testability for single fault detection in two-dimensional systolic array structures for matrix multiplication

10.1109/iscas.1990.112573 ◽

2002 ◽

Cited By ~ 2

Author(s):

F. Lombardi ◽

D. Sciuto ◽

W. Huang

Keyword(s):

Fault Detection ◽

Systolic Array ◽

Matrix Multiplication ◽

Two Dimensional ◽

Single Fault ◽

Array Structures

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Single Fault Detection and Diagnosis Technique for Digital Micro-Fluidic Based Biochips

Computer Science & Information Technology ( CS & IT ) ◽

10.5121/csit.2013.3404 ◽

2013 ◽

Author(s):

Sagarika Chowdhury ◽

Sumitava Roy ◽

Sourav Saha ◽

Arijit Saha

Keyword(s):

Fault Detection ◽

Fault Detection And Diagnosis ◽

Single Fault ◽

Detection And Diagnosis ◽

Diagnosis Technique

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ON LOGIC NETWORKS ALLOWING SHORT SINGLE FAULT DETECTION TESTS UNDER ARBITRARY FAULTS OF GATES

PRIKLADNAYa DISKRETNAYa MATEMATIKA ◽

10.17223/20710410/51/4 ◽

2021 ◽

pp. 85-100

Author(s):

K. A. Popkov ◽

Keyword(s):

Fault Detection ◽

Boolean Function ◽

Logic Gates ◽

Single Fault ◽

Logic Network

It is proved that one can implement any non-constant Boolean function in n variables by an irredundant logic network in the basis {&, ⊕, ¬}, containing not more than one dummy input variable and allowing a single fault detection test with length not more than 2n + 3 regarding arbitrary faults of logic gates.

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