On the complexity of multivalued logic functions over some infinite basisстатья
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Дата последнего поиска статьи во внешних источниках: 5 августа 2018 г.
Аннотация:Under study is the complexity of the realization of k-valued logic functions (k ≥ 3) by
logic circuits in the infinite basis consisting of the Post negation (i.e., the function (x + 1) mod k)
and all monotone functions. The complexity of the circuit is the total number of elements of this
circuit. For an arbitrary function f, we find the lower and upper bounds of complexity, which differ
from one another at most by 1 and have the form3 log_3(d(f)+ 1)+O(1), where d(f) is the maximal
number of the decrease of the value of f taken over all increasing chains of tuples of values of the
variables. We find the exact value of the corresponding Shannon function which characterizes the
complexity of the most complex function of a given number of variables.