Related papers: The genus of regular languages
We establish a Myhill-Nerode type theorem for higher-dimensional automata (HDAs), stating that a language is regular if and only if it has finite prefix quotient. HDAs extend standard automata with additional structure, making it possible…
An introductory formal languages course exposes advanced undergraduate and early graduate students to automata theory, grammars, constructive proofs, computability, and decidability. Programming students find these topics to be challenging…
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…
This work studies the question of learning probabilistic deterministic automata from language models. For this purpose, it focuses on analyzing the relations defined on algebraic structures over strings by equivalences and similarities on…
In automata theory, while determinisation provides a standard route to solving many common problems in automata theory, some weak forms of nondeterminism can be dealt with in some problems without costly determinisation. For example, the…
The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration…
Let $\mathcal{P}(\Sigma^*)$ be the semiring of languages, and consider its subset $\mathcal{P}(\Sigma)$. In this paper we define the language recognized by a weighted automaton over $\mathcal{P}(\Sigma)$ and a one-letter alphabet.…
We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language -- which is the number of its (left) quotients, and…
Families of DFAs (FDFAs) provide an alternative formalism for recognizing $\omega$-regular languages. The motivation for introducing them was a desired correlation between the automaton states and right congruence relations, in a manner…
Arden's Lemma is a classical result in language theory allowing the computation of a rational expression denoting the language recognized by a finite string automaton. In this paper we generalize this important lemma to the rational tree…
The recent successes and spread of large neural language models (LMs) call for a thorough understanding of their computational ability. Describing their computational abilities through LMs' \emph{representational capacity} is a lively area…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
Recurrent neural networks (RNNs) have reached striking performance in many natural language processing tasks. This has renewed interest in whether these generic sequence processing devices are inducing genuine linguistic knowledge. Nearly…
We consider some questions about formal languages that arise when inverses of letters, words and languages are defined. The reduced representation of a language over the free monoid is its unique equivalent representation in the free group.…
We investigate families of infinite automata for context-sensitive languages. An infinite automaton is an infinite labeled graph with two sets of initial and final vertices. Its language is the set of all words labelling a path from an…
A regular language is $k$-lookahead deterministic (resp. $k$-block deterministic) if it is specified by a $k$-lookahead deterministic (resp. $k$-block deterministic) regular expression. These two subclasses of regular languages have been…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
Grammatical inference consists in learning a formal grammar (as a set of rewrite rules or a finite state machine). We are concerned with learning Nondeterministic Finite Automata (NFA) of a given size from samples of positive and negative…
Grammatical inference consists in learning a formal grammar as a finite state machine or as a set of rewrite rules. In this paper, we are concerned with inferring Nondeterministic Finite Automata (NFA) that must accept some words, and…
Indexing strings via prefix (or suffix) sorting is, arguably, one of the most successful algorithmic techniques developed in the last decades. Can indexing be extended to languages? The main contribution of this paper is to initiate the…