Lower bounds for lengths of single tests for Boolean circuits

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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Lower bounds for lengths of single tests for Boolean circuits

Abstract: We obtain nontrivial lower bounds for lengths of minimal single fault detection and diagnostic tests for Boolean circuits in wide classes of bases in presence of stuck-at faults at outputs of circuit gates.

Cited by 3 publications

References 8 publications

The Length of Single-Fault Detection Tests with Respect to Substitution of Inverters for Combinational Elements in Some Bases

The Length of Single-Fault Detection Tests with Respect to Substitution of Inverters for Combinational Elements in Some Bases

The Length of Single Fault Detection Tests with Respect to Substitution of Gates with Inverters

Short single tests for circuits with arbitrary stuck-at faults at outputs of gates

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