Geodesic
Implementation of Linear Boolean Functions by Self-Correcting Circuits of Unreliable Logic Gates
Matematičeskie zametki, Tome 115 (2024) no. 1, pp. 91-107

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We prove that if a Boolean function essentially depends on at least two variables, then it cannot be implemented by a circuit that consists of unreliable gates with at most two inputs each and is self-correcting with respect to at least some faults of an arbitrary number of gates. In view of the previous results, it suffices to establish this fact for linear functions.
Keywords: logic circuit, self-correction, unreliable gate, linear Boolean function. 
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     author = {K. A. Popkov},
     title = {Implementation of {Linear} {Boolean} {Functions} by {Self-Correcting} {Circuits} of {Unreliable} {Logic} {Gates}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {91--107},
     publisher = {mathdoc},
     volume = {115},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2024_115_1_a6/}
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K. A. Popkov. Implementation of Linear Boolean Functions by Self-Correcting Circuits of Unreliable Logic Gates. Matematičeskie zametki, Tome 115 (2024) no. 1, pp. 91-107. http://geodesic.mathdoc.fr/item/MZM_2024_115_1_a6/