Given a class K of partial Boolean functions and a partial Boolean function f of n variables, a subset U of its variables is called sufficient for the implementation of f in K if there exists an extension of f in K with arguments in U. We consider the problem of recognizing all subsets sufficient for the implementation of f in K. For some classes defined by relations, we propose the algorithms of solving this problem with complexity of O(2ⁿn²) bit operations. In particular, we present some algorithms of this complexity for the class P^*₂ of all partial Boolean functions and the class M^*₂ of all monotone partial Boolean functions. The proposed algorithms use the Walsh-Hadamard and Möbius transforms.

中文翻译：

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查找部分布尔函数的变量子集，这些变量子集足以在谓词定义的类中实现

给定一类ķ的局部布尔函数和局部布尔函数˚F的Ñ变量，子集ü其变量被称为足够对于f的K中执行，如果存在一个的延伸˚F在ķ与参数ü。我们考虑识别所有子集足以在K中实现f的问题。对于由关系定义的某些类，我们提出了以O（2 ⁿ n ²）位操作。特别是，我们为所有部分布尔函数的P ^* ₂类和所有单调部分布尔函数的M ^* ₂类提供了这种复杂性的一些算法。提出的算法使用Walsh-Hadamard和Möbius变换。