Related papers: Tree Automata and Tree Grammars
A theory of how agents can come to understand a language is presented. If understanding a sentence $\alpha$ is to associate an operator with $\alpha$ that transforms the representational state of the agent as intended by the sender, then…
We introduce Transformer Grammars (TGs), a novel class of Transformer language models that combine (i) the expressive power, scalability, and strong performance of Transformers and (ii) recursive syntactic compositions, which here are…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…
Transfer learning is a vital technique that generalizes models trained for one setting or task to other settings or tasks. For example in speech recognition, an acoustic model trained for one language can be used to recognize speech in…
A deterministic finite automaton in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize such automata in terms of graphs…
We study finite automata running over infinite binary trees. A run of such an automaton is usually said to be accepting if all its branches are accepting. In this article, we relax the notion of accepting run by allowing a certain quantity…
In the following pages we discuss infinite sequences defined on a finite alphabet, and more specially those which are generated by finite automata. We have divided our paper into seven parts which are more or less self-contained. Needless…
Separation Logic (SL) with inductive definitions is a natural formalism for specifying complex recursive data structures, used in compositional verification of programs manipulating such structures. The key ingredient of any automated…
We consider the synthesis of deterministic tree transducers from automaton definable specifications, given as binary relations, over finite trees. We consider the case of specifications that are deterministic top-down tree automatic,…
Finite-state tree automata are a well studied formalism for representing term languages. This paper studies the problem of determining the regularity of the set of instances of a finite set of terms with variables, where each variable is…
A new class of languages of infinite words is introduced, called the max-regular languages, extending the class of $\omega$-regular languages. The class has two equivalent descriptions: in terms of automata (a type of deterministic counter…
This article is an introduction to formal languages from the point of view of combinatorial group theory. Group theoretic applications are included and language classes are defined algebraically.
We consider the previously defined notion of finite-state independence and we focus specifically on normal words. We characterize finite-state independence of normal words in three different ways, using three different kinds of asynchronous…
It is proved that the family of tree languages recognized by nondeterministic tree-walking automata is not closed under complementation, solving a problem raised by Boja\'nczyk and Colcombet ("Tree-walking automata do not recognize all…
Most Formal Languages and Automata Theory courses explore the duality between computation models to recognize words in a language and computation models to generate words in a language. For students unaccustomed to formal statements, these…
In this paper, we study First Order Logic (FO) over (unordered) infinite trees and its connection with branching-time temporal logics. More specifically, we provide an automata-theoretic characterisation of FO interpreted over infinite…
The use of terms from natural and social scientific titles and abstracts is studied from the perspective of sublanguages and their specialized dictionaries. Different notions of sublanguage distinctiveness are explored. Objective methods…
Multiple (simple) context-free tree grammars are investigated, where "simple" means "linear and nondeleting". Every multiple context-free tree grammar that is finitely ambiguous can be lexicalized; i.e., it can be transformed into an…
We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…
Nobody knows how language works, but many theories abound. Transformers are a class of neural networks that process language automatically with more success than alternatives, both those based on neural computations and those that rely on…