Constituency Parsing as an Instance of the M-monoid Parsing Problem

We consider the constituent parsing problem which states: given a final state normalized constituent tree automaton (CTA) and a string, compute the set of all constituent trees that are inductively recognized by the CTA and yield the string. We show that this problem is an instance of the M-monoid parsing problem. Moreover, we show that we can employ the generic M-monoid parsing algorithm to solve the constituency parsing problem for a meaningful class of CTA.Comment: In Proceedings NCMA 2023, arXiv:2309.0733

Logics and Automata for Totally Ordered Trees

A totally ordered tree is a tree equipped with an additional total order on its nodes. It provides a formal model for data that comes with both a hierarchical and a sequential structure; one example for such data are natural language sentences, where a sequential structure is given by word order, and a hierarchical structure is given by grammatical relations between words. In this paper, we study monadic second-order logic (MSO) for totally ordered terms. We show that the MSO satisfiability problem of unrestricted structures is undecidable, but give a decision procedure for practically relevant sub-classes, based on tree automata