Related papers: A Descriptive Characterization of Tree-Adjoining L…
Grounding natural language in images, such as localizing "the black dog on the left of the tree", is one of the core problems in artificial intelligence, as it needs to comprehend the fine-grained and compositional language space. However,…
Evaluating the quality of reasoning traces from large language models remains understudied, labor-intensive, and unreliable: current practice relies on expert rubrics, manual annotation, and slow pairwise judgments. Automated efforts are…
We study the question of whether a given regular language of finite trees can be defined in first-order logic. We develop an algebraic approach to address this question and we use it to derive several necessary and sufficient conditions for…
The development of lexicalized grammars, particularly Tree-Adjoining Grammar (TAG), has significantly advanced our understanding of syntax and semantics in natural language processing (NLP). While existing syntactic resources like the Penn…
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…
A natural next step in the evolution of constraint-based grammar formalisms from rewriting formalisms is to abstract fully away from the details of the grammar mechanism---to express syntactic theories purely in terms of the properties of…
The starting point of algebraic language theory is that regular languages of finite words are exactly those recognized by finite monoids. This finiteness condition gives rise to a topological space whose points, called profinite words,…
Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…
A tree automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. Words can be regarded as specific…
Weir has defined a hierarchy of language classes whose second member ($\mathcal{L}_2$) is generated by tree-adjoining grammars (TAG), linear indexed grammars (LIG), combinatory categorial grammars, and head grammars. The hierarchy is…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
We define a class of ranked tree automata TABG generalizing both the tree automata with local tests between brothers of Bogaert and Tison (1992) and with global equality and disequality constraints (TAGED) of Filiot et al. (2007). TABG can…
The definition of graph automatic groups by Kharlampovich, Khoussainov and Miasnikov and its extension to C-graph automatic by Murray Elder and the first author raise the question of whether Thompson's group F is graph automatic. We define…
This paper deals with graph automaton groups associated with trees and some generalizations. We start by showing some algebraic properties of tree automaton groups. Then we characterize the associated semigroup, proving that it is…
We consider the state complexity of basic operations on tree languages recognized by deterministic unranked tree automata. For the operations of union and intersection the upper and lower bounds of both weakly and strongly deterministic…
When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…
In this article, we present a fresh perspective on language, combining ideas from various sources, but mixed in a new synthesis. As in the minimalist program, the question is whether we can formulate an elegant formalism, a universal…
It is well known that for a regular tree language it is decidable whether or not it can be recognized by a deterministic top-down tree automaton (DTA). However, the computational complexity of this problem has not been studied. We show that…
We study trees where each successor set is equipped with some additional structure. We introduce a family of automaton models for such trees and prove their equivalence to certain fixed-point logics. As a consequence we obtain…
Dependency syntax represents the structure of a sentence as a tree composed of dependencies, i.e., directed relations between lexical units. While in its more general form any such tree is allowed, in practice many are not plausible or are…