关于布尔函数的复合闭类
On composition-closed classes of Boolean functions
摘要：
我们确定了布尔函数的所有复合闭方程类。这些类提供了克隆和迭代代数的自然推广：它们在变量的组合、置换和识别（对角化）以及引入非本质变量（圆柱化）下是封闭的，但它们不一定包含投影。因此，由这些类形成的格是Post格的扩展。这个格的基数是连续的，但在某种程度上可以描述它的结构。
英文摘要：
We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification (diagonalization) of variables and under introduction of inessential variables (cylindrification), but they do not necessarily contain projections. Thus the lattice formed by these classes is an extension of the Post lattice. The cardinality of this lattice is continuum, yet it is possible to describe its structure to some extent.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
