Related papers: Construction of rational expression from tree auto…
Language models (LMs) are often expected to generate strings in some formal language; for example, structured data, API calls, or code snippets. Although LMs can be tuned to improve their adherence to formal syntax, this does not guarantee…
We prove that $\omega$-regular languages accepted by B\"uchi or Muller automata satisfy an effective automata-theoretic version of the Baire property. Then we use this result to obtain a new effective property of rational functions over…
In this paper we consider the class of lambda-nondeterministic linear automata as a model of the class of linear languages. As usual in other automata models, lambda-moves do not increase the acceptance power. The main contribution of this…
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…
The notion of abstract Boehm tree has arisen as an operationally-oriented distillation of works on game semantics, and has been investigated in two papers. This paper revisits the notion, providing more syntactic support and more examples…
In this paper, we extend the notion of (word) derivatives and partial derivatives due to (respectively) Brzozowski and Antimirov to tree derivatives using already known inductive formulae of quotients. We define a new family of extended…
This paper introduces derivation trees for general grammars. Within these trees, it defines context-dependent pairs of nodes, corresponding to rewriting two neighboring symbols using a non context-free rule. It proves that the language…
Automata learning is a popular technique used to automatically construct an automaton model from queries. Much research went into devising ad hoc adaptations of algorithms for different types of automata. The CALF project seeks to unify…
We show that the set of all formulas in n variables valid in a finite class A of finite algebras is always a regular tree language, and compute a finite axiom set for A. We give a rational reconstruction of Barzdins' liquid flow algorithm…
Natural languages are complexly structured entities. They exhibit characterising regularities that can be exploited to link them one another. In this work, I compare two morphological aspects of languages: Written Patterns and Sentence…
Analogous to regular string and tree languages, regular languages of directed acyclic graphs (DAGs) are defined in the literature. Although called regular, those DAG-languages are more powerful and, consequently, standard problems have a…
We describe here a simple application of rational trees to the implementation of an interpreter for a procedural language written in a logic programming language. This is possible in languages designed to support rational trees (such as…
The aim of this paper is to design the polynomial construction of a finite recognizer for hairpin completions of regular languages. This is achieved by considering completions as new expression operators and by applying derivation…
A leaf path language is a Boolean combination of sets of the form $\mathsf{{}^mE}^k L$, with $k \ge 1$ and $L$ a regular word language, which consist of those forests where the node labels in at least $k$ leaf-to-root paths make up a word…
We develop a fully diagrammatic approach to the theory of finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. Moreover, we provide an…
This paper describes a neural semantic parser that maps natural language utterances onto logical forms which can be executed against a task-specific environment, such as a knowledge base or a database, to produce a response. The parser…
Kleene algebra (KA) is an important tool for reasoning about general program equivalences, with a decidable and complete equational theory. However, KA cannot always prove equivalences between specific programs. For this purpose, one adds…
This paper develops a natural-language agent-based model of argumentation (ABMA). Its artificial deliberative agents (ADAs) are constructed with the help of so-called neural language models recently developed in AI and computational…
The precise formulation of derivation for tree-adjoining grammars has important ramifications for a wide variety of uses of the formalism, from syntactic analysis to semantic interpretation and statistical language modeling. We argue that…
Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free…