The stationary characteristics of gain-guiding semiconductor lasers with a symmetrical structure are theoretically examined, solving the wave equation by the Galerkins method and taking the effect of transverse carrier diffusion into consideration. For wide stripe lasers, the carrier density distribution becomes flat with the increase of the current density. And with the more increase of the current density, a hole-burning, a mode deformation and a kink" in the current density-light output characteristics appear. For the narrower stripe lasers, the current density where the hole-burning occurs increases and surpasses the normal driving current level. Hence the transverse mode profile can be approximated by the gaussian one with a small numerical error, which verifies the assumption in our previous papers^(8),(9). The influence of the current profile on the characteristics is larger for wide stripe lasers than for narrow ones. However it less affects them compared with the transverse carrier diffusion even for wide stripe lasers. That is, the effect of current density profiles on the characteristics is weakened by the transverse carrier diffusion.

Various minimization problems associated with the diagnosis of systems represented by directed graphs are shown to be NP-complete. These problems include () finding the minimum number of test points, test connections and blocking gates on a SEC graph (single entry single exit connected acyclic graph), respectively, to make it distinguishable, and () finding a test set with the minimum number of tests to locate a faulty vertex on a SEC graph with test points, test connections and blocking gates attached, respectively. The NP-completeness results indicate that these problems are all intractable in the sense that it is most unlikely that some algorithm can solve them in polynomial time of the problem size.