Geodesic
A lower bound for the complexity of generalized parallel-serial contact circuits for a~characteristic function of divisibility by~$q$
Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 6, pp. 68-76

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We consider generalization of the concept of a parallel-serial contact circuit in the case when the variables assigned to contacts can take not two as in the Boolean case but a greater number of values. The conductivity of contacts as well as in the Boolean case remains two-valued (a contact is either close or break). We obtain a lower bound for the complexity of such circuits computing the characteristic function of divisibility by $q$, i.e., the function $\varphi_q\colon\{0,1,\dots,q-1\}^n\to\{0,1\}$ which is equal to 1 if the sum of values of its variables is divided by $q$. Bibliogr. 6.
Keywords: Boolean function, complexity of circuits.
Mots-clés : contact circuit 
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     author = {K. L. Rychkov},
     title = {A lower bound for the complexity of generalized parallel-serial contact circuits for a~characteristic function of divisibility by~$q$},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {68--76},
     publisher = {mathdoc},
     volume = {17},
     number = {6},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2010_17_6_a4/}
}
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K. L. Rychkov. A lower bound for the complexity of generalized parallel-serial contact circuits for a~characteristic function of divisibility by~$q$. Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 6, pp. 68-76. http://geodesic.mathdoc.fr/item/DA_2010_17_6_a4/