Abstract

The problem of determining the nonmonotone complexity of the implementation of \(k\)-valued logic functions by logic circuits in bases consisting of all monotone (with respect to the standard order) functions and finitely many nonmonotone functions is investigated. In calculating the complexity measure under examination only those elements of the circuit which are assigned nonmonotone basis functions are taken into account. The nonmonotone complexity of an arbitrary \(k\)-valued logic function is determined with high accuracy, namely, upper and lower bounds which differ by a constant not exceeding \(3 \log_2 k+4\) are found.

中文翻译：

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$$k$$ 值逻辑函数的非单调复杂度估计的改进

摘要

研究了确定由所有单调（相对于标准阶）函数和有限多个非单调函数组成的基中的逻辑电路实现k值逻辑函数的非单调复杂度的问题。在计算所检查的复杂性度量时，仅考虑那些分配有非单调基函数的电路元件。高精度确定任意\(k\)值逻辑函数的非单调复杂度，即找到相差不超过\(3 \log_2 k+4\)常数的上下界。