用于公用控制件的二元周期序列的组合计数

应用科学学报 ›› 1995, Vol. 13 ›› Issue (3): 327-332.

用于公用控制件的二元周期序列的组合计数

王启义, 阎喜仁

东北大学

收稿日期:1993-02-15 修回日期:1994-11-23 出版日期:1995-09-30 发布日期:1995-09-30
基金资助:
国家自然科学基金资助项目

COMBINATORIAL COUNTING OF BINARY CYCLIC SEQUENCES APPLIEDTOSHARED CONTROLLERS

WANG QIYI, YAN XIREN

Northeastern University

Received:1993-02-15 Revised:1994-11-23 Online:1995-09-30 Published:1995-09-30

摘要/Abstract

摘要： 该文以组合计数理论为基础,推导出排除等价序列和排除子周期序列的本原周期序列数目计算公式,并给出高效算法,使搜寻公用控制方案中可用序列的基序列数目约缩为全部的1/4.同时,给出自互反、自互补和自互反补序列的计数公式,又应用Stirling渐近公式求出当序列周期较大时各种特殊序列数目的比例关系。所导出的公式不仅完善了公用控制理论,而且使长周期可用序列的搜寻工作量减小近3/4。

关键词: 二元周期序列, 公用控制件, 组合计数

Abstract: Binary cyclic sequences have been widely used in the research on shared cont-rollers. The point is:that an usable sequence represents a usable scheme of the shared controller, However,to search for all the usable sequences,the old methods have to take all the primitive cyclic sequences as their basic sequences and remove unu-sable sequences from the basic ones.In fact,these basic sequences contain a large number of equivalent sequences and sub-cyclic sequences which are definitely unusable,and removal of these sequences will save considerable amount of calcu-lations.

Key words: shared controller, combinatorial coun-ting, binary cyclio sequence

王启义, 阎喜仁. 用于公用控制件的二元周期序列的组合计数[J]. 应用科学学报, 1995, 13(3): 327-332.

WANG QIYI, YAN XIREN. COMBINATORIAL COUNTING OF BINARY CYCLIC SEQUENCES APPLIEDTOSHARED CONTROLLERS[J]. Journal of Applied Sciences, 1995, 13(3): 327-332.