The Number of Registers Required for Evaluating Arithmetic Expressions
The Number of Registers Required for Evaluating Arithmetic Expressions
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计算算术表达式所需的寄存器数量
DOI：
10.1016/0304-3975(79)90009-4
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发表时间：
1979
期刊：
影响因子：
--
通讯作者：
J. Vuillemin
中科院分区：
文献类型：
--
作者：
P. Flajolet;J. Raoult;J. Vuillemin
我们研究计算算术表达式所需的寄存器数量。二叉树的这个参数出现在各种计算机科学问题以及许多自然科学应用中，被称为斯特拉勒数。我们给出了几个描述大小树的寄存器数量分布的枚举结果。寄存器的平均数量具有渐近展开式 log4n+D(log4n) + 0(1)；这里，函数Dis是第一周期的周期函数，其傅里叶展开式可以根据黎曼zeta函数和欧拉gamma函数明确确定。
We study the number of registers required for evaluating arithmetic expressions. This parameter of binary trees appears in various computer science problems as well as in numerous natural sciences applications where it is known as the Strahler number.We give several enumeration results describing the distribution of the number of registers for trees of sizen. The average number of registers has the asymptotic expansion log4n+D(log4n) + 0(1); here, functionDis periodic of period one, and its Fourier expansion can be explicitly determined in terms of Riemann's zeta function and Euler's gamma function.