General 2-path Problem

Abstract

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.