The problem of identifying a probabilistic context free grammar has two
aspects: the first is determining the grammar's topology (the rules of the
grammar) and the second is estimating probabilistic weights for each rule.
Given the hardness results for learning context-free grammars in general, and
probabilistic grammars in particular, most of the literature has concentrated
on the second problem. In this work we address the first problem. We restrict
attention to structurally unambiguous weighted context-free grammars (SUWCFG)
and provide a query learning algorithm for \structurally unambiguous
probabilistic context-free grammars (SUPCFG). We show that SUWCFG can be
represented using \emph{co-linear multiplicity tree automata} (CMTA), and
provide a polynomial learning algorithm that learns CMTAs. We show that the
learned CMTA can be converted into a probabilistic grammar, thus providing a
complete algorithm for learning a structurally unambiguous probabilistic
context free grammar (both the grammar topology and the probabilistic weights)
using structured membership queries and structured equivalence queries. A
summarized version of this work was published at AAAI 21.

本篇文章研究了如何用查询学习算法解决确定性上下文自由文法的拓扑结构问题，提出了一种基于多重树状自动机算法的结构明确概率上下文自由文法学习方法，这种方法既可以学习语法的拓扑结构又可以学习概率权重，同时还给出了相应的结构化成员查询和结构等价查询算法。