Geodesic
On checking tests for a parity counter
Diskretnaya Matematika, Tome 7 (1995) no. 4, pp. 51-59
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We consider the circuits of functional elements realizing the Boolean function $$ f^{\oplus }_{n}(\tilde{x})=x_{1}\oplus x_{2}\oplus \ldots \oplus x_{n} $$ under arbitrary constant failures on the inputs of elements. It is proved that for such circuits the length of the complete checking test is no less than $n+1$. It is shown that there exists a circuit realizing $f^{\oplus }_{n}(\tilde{x})$ with the complete checking test of length $n+2$. 
@article{DM_1995_7_4_a3,
     author = {V. G. Khakhulin},
     title = {On checking tests for a parity counter},
     journal = {Diskretnaya Matematika},
     pages = {51--59},
     year = {1995},
     volume = {7},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1995_7_4_a3/}
}
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V. G. Khakhulin. On checking tests for a parity counter. Diskretnaya Matematika, Tome 7 (1995) no. 4, pp. 51-59. http://geodesic.mathdoc.fr/item/DM_1995_7_4_a3/