Related papers: Regular languages, derivatives and finite automata
The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present paper we tour a fragment of the literature and summarize results on…
We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying…
Splicing as a binary word/language operation is inspired by the DNA recombination under the action of restriction enzymes and ligases, and was first introduced by Tom Head in 1987. Shortly thereafter, it was proven that the languages…
The regular languages with a neutral letter expressible in first-order logic with one alternation are characterized. Specifically, it is shown that if an arbitrary $\Sigma_2$ formula defines a regular language with a neutral letter, then…
In this chapter we discuss the problem of enumerating distinct regular expressions by size and the regular languages they represent. We discuss various notions of the size of a regular expression that appear in the literature and their…
Passive documents and active programs now widely comingle. Document languages include Turing-complete programming elements, and programming languages include sophisticated document notations. However, there are no formal foundations that…
In natural language, words and phrases themselves imply the semantics. In contrast, the meaning of identifiers in mathematical formulae is undefined. Thus scientists must study the context to decode the meaning. The Mathematical Language…
In this paper we regard languages and their acceptors -- such as deterministic or weighted automata, transducers, or monoids -- as functors from input categories that specify the type of the languages and of the machines to categories that…
Creating a descriptive grammar of a language is an indispensable step for language documentation and preservation. However, at the same time it is a tedious, time-consuming task. In this paper, we take steps towards automating this process…
Foundations of formal languages, as subfield of theoretical computer science, are part of typical upper secondary education curricula. There is very little research on the potential difficulties that students at this level have with this…
Automata-logic connections are pillars of the theory of regular languages. Such connections are harder to obtain for transducers, but important results have been obtained recently for word-to-word transformations, showing that the three…
Futrell and Mahowald (2025) frame the success of neural language models (LMs) as supporting gradient, usage-based linguistic theories. I argue that LMs can also instantiate theories based on formal structures - the types of theories seen in…
"Natural Language," whether spoken and attended to by humans, or processed and generated by computers, requires networked structures that reflect creative processes in semantic, syntactic, phonetic, linguistic, social, emotional, and…
Automata over infinite words, also known as omega-automata, play a key role in the verification and synthesis of reactive systems. The spectrum of omega-automata is defined by two characteristics: the acceptance condition (e.g. B\"uchi or…
In historical linguistics, the affiliation of languages to a common language family is traditionally carried out using a complex workflow that relies on manually comparing individual languages. Large-scale standardized collections of…
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…
We present two novel approaches to parsing context-free languages. The first approach is based on an extension of Brzozowski's derivative from regular expressions to context-free grammars. The second approach is based on a generalization of…
This paper presents the main features of a system that aims to transform regular expressions into shorter equivalent expressions. The system is also capable of computing other operations useful for simplification, such as checking the…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
Large language models (LLMs) are a promising venue for natural language understanding and generation tasks. However, current LLMs are far from reliable: they are prone to generate non-factual information and, more crucially, to contradict…