Geodesic
On the complexity of generalized contact circuits
Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 5, pp. 78-87

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We consider generalizations of the concepts of a contact circuit and a parallel-serial contact circuit in the case when the variables assigned to contacts can accept not two as in a Boolean case, but a greater number of values. The conductivity of contacts as well as in a Boolean case remains two-valued (a contact either will close, or will break). We have obtained upper and lower bounds on the complexity of such circuits computing a function $f\colon\{0,1,\dots,q-1\}^n\to\{0,1\}$ which accepts the value 1 at a vector $(\delta_1,\dots,\delta_n)\in\{0,1,\dots,q-1\}^n$ if $\delta_1+\dots+\delta_n\neq0\pmod q$. Bibl. 9.
Keywords: Boolean function, complexity of circuits.
Mots-clés : contact circuit 
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     author = {K. L. Rychkov},
     title = {On the complexity of generalized contact circuits},
     journal = {Diskretnyj analiz i issledovanie operacij},
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     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/DA_2009_16_5_a7/}
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K. L. Rychkov. On the complexity of generalized contact circuits. Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 5, pp. 78-87. http://geodesic.mathdoc.fr/item/DA_2009_16_5_a7/