Weakly restricted stochastic grammars

A new type of stochastic grammars in introduced for investigation: weakly restricted stochastic grammars. In this paper we will concentrate on the consistency problem. To find conditions for stochastic grammars to be consistent, the theory of multitype Galton-Watson brancning processes and generating functions is of central importance. The unrestricted stochastic grammar formalism generates the same class of languages as the weakly restricted formalism. The inside-outside algorithm is adapted for use with weakly restricted grammars.