  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.
