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及计算复杂度的相关基础知识。为综合一般双路径问题在F(z)上的充要条件，其次分别分析了该问题在F(z)或R上的充分条件以及在F(z)上的必要条件。此外，深入推导出关于R是否存在一般双路径的等价充要条件。最后，介绍了该等价充要条件对应算法的计算复杂度，表明一般双路径问题属于P类问题。