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.

我们将句法随机过程 (SSP) 定义为在语法的终结符号集中取值的随机过程，其实现是由某些随机语法生成的终结字符串。并表明由随机上下文无关文法 (SCFG) 生成的任何 SSP 都可以由适当定义的图形随机场 (GRF) 的节点子集一致地索引。在论文的第二部分，我们提出了随机上下文敏感语法 (SCSG) 的定义，并且由 SCFG 生成的随机过程允许表示为 GRF。最后，我们展示了由随机树邻接文法 (STAG) 生成的字符串是互惠过程，这允许解决推理问题的复杂度与字符串长度成线性关系。