On a Matrix of First Moments for Decomposable Stochastic CF-Grammar

Stochastic context-free grammar is considered which contains arbitrary number of classes of non-terminal symbols without restrictions on the succession order of classes. Corresponding matrix $A$ of first moments is decomposable. For the case when Perron's root of the matrix $A$ is strictly less than one, properties of the matrix $A^t$ are investigated under $t\to\infty$.