In this paper, some preliminaries about signal flow graph, linear time-invariant system on F(z) and computational complexity are first introduced in detail. In order to synthesize the necessary and sufficient condition on F(z) for a general 2-path problem, the sufficient condition on F(z) or R and necessary conditions on F(z) for a general 2-path problem are secondly analyzed respectively. Moreover, an equivalent sufficient and necessary condition on R whether there exists a general 2-path is deduced in detail. Finally, the computational complexity of the algorithm for this equivalent sufficient and necessary condition is introduced so that it means that the general 2-path problem is a P problem.
翻译:本文首先详细介绍了信号流图、F(z)上的线性时不变系统以及计算复杂度等方面的一些基础知识。为了综合F(z)上的必要和充分条件,分别分析了通用2路径问题在F(z)上的充分条件和必要条件。此外,还详细推导了R上是否存在通用2路径的等价充分必要条件。最后,介绍了等价充分必要条件的算法计算复杂度,表明通用2路径问题是一个P问题。