Syntactic stochastic processes: Definitions, models, and related inference problems

We define a Syntactic Stochastic Process (SSP) as a stochastic process valued in the set of terminal symbols of a grammar, and whose realizations are terminal strings generated by some stochastic grammar. and show that any SSP generated by a Stochastic Context Free Grammar (SCFG) can be consistently indexed by a subset of nodes of a suitable defined Graphical Random Field (GRF). In the second part of the paper we propose a definition of Stochastic Context-Sensitive Grammar (SCSG), and that the stochastic process generated by a SCFG admits a representation as a GRF. Finally, we show that strings generated by a Stochastic Tree Adjoining Grammar (STAG) are reciprocal processes, which allows the solution of the inference problem with a complexity linear with respect to string length.