论文标题
关于M {Ö} Bius变换的计算
On the computation of the M{ö}bius transform
论文作者
论文摘要
M {Ö} Bius变换是向布尔世界的关键转变。 它允许更改真实表和代数正常形式之间的布尔表示。 在这项工作中，我们基于布尔函数的多项式形式介绍了这种转换的新代数观点。 看来我们可以执行一个新的概念：通过变量和新计算属性的m {Ö} BIUS计算变量。 结果，我们提出了新算法，这些算法可以为布尔函数的亚元素产生M {Ö} Bius计算的巨大速度。 此外，我们直接计算某些特定布尔函数的m {Ö} BIUS转换。 最后，我们表明，对于其中的一些，锤子的重量与代数的特定因素直接相关。
The M{ö}bius transform is a crucial transformation into the Boolean world; it allows to change the Boolean representation between the True Table and Algebraic Normal Form. In this work, we introduce a new algebraic point of view of this transformation based on the polynomial form of Boolean functions. It appears that we can perform a new notion: the M{ö}bius computation variable by variable and new computation properties. As a consequence, we propose new algorithms which can produce a huge speed up of the M{ö}bius computation for sub-families of Boolean function. Furthermore we compute directly the M{ö}bius transformation of some particular Boolean functions. Finally, we show that for some of them the Hamming weight is directly related to the algebraic degree of specific factors.
