Related papers: A Categorical Approach to Syntactic Monoids

Assume that $X= {x_1,...,x_g}$ is a finite alphabet and $K$ is a field. We study monomial algebras $A= K <X> /(W)$, where $W$ is an antichain of Lyndon words in $X$ of arbitrary cardinality. We find a Poincar\'{e}-Birkhoff-Witt type basis…

In previous work ("From signatures to monads in UniMath"), we described a category-theoretic construction of abstract syntax from a signature, mechanized in the UniMath library based on the Coq proof assistant. In the present work, we…

The goal of the present paper is to provide a systematic and comprehensive study of rational stochastic languages over a semiring K \in {Q, Q +, R, R+}. A rational stochastic language is a probability distribution over a free monoid…

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a…

We give a 3-categorical, purely formal argument explaining why on the category of Kleisli algebras for a lax monoidal monad, and dually on the category of Eilenberg-Moore algebras for an oplax monoidal monad, we always have a natural…

We give an exposition of the semantics of the simply-typed lambda-calculus, and its linear and ordered variants, using multi-ary structures. We define universal properties for multicategories, and use these to derive familiar rules for…

We present a simple technique for semantic, open logical relations arguments about languages with recursive types, which, as we show, follows from a principled foundation in categorical semantics. We demonstrate how it can be used to give a…

The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…

We investigate two operators on classes of regular languages: polynomial closure (Pol) and Boolean closure (Bool). We apply these operators to classes of group languages G and to their well-suited extensions G+, which is the least Boolean…

Languages may encode similar meanings using different sentence structures. This makes it a challenge to provide a single set of formal rules that can derive meanings from sentences in many languages at once. To overcome the challenge, we…

For predual categories C and D we establish isomorphisms between opfibrations representing local varieties of languages in C, local pseudovarieties of D-monoids, and finitely generated profinite D-monoids. The global sections of these…

The paper explains the connection between topological theories for one-manifolds with defects and values in the Boolean semiring and automata and their generalizations. Finite state automata are closely related to regular languages. To each…

The classical subset construction for non-deterministic automata can be generalized to other side-effects captured by a monad. The key insight is that both the state space of the determinized automaton and its semantics---languages over an…

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…

Clones are specializations of operads forming powerful instruments to describe varieties of algebras wherein repeating variables are allowed in their equations. They allow us in this way to realize and study a large range of algebraic…

We give a finite axiomatization for the variety generated by relational, integral ordered monoids. As a corollary we get a finite axiomatization for the language interpretation as well.

We give a domain-theoretic semantics to a statistical programming language, using the plain old category of dcpos, in contrast to some more sophisticated recent proposals. Remarkably, our monad of minimal valuations is commutative, which…

We propose a generic categorical framework for learning unknown formal languages of various types (e.g. finite or infinite words, weighted and nominal languages). Our approach is parametric in a monad T that represents the given type of…

Szlach\'anyi's skew monoidal categories are a well-motivated variation of monoidal categories in which the unitors and associator are not required to be natural isomorphisms, but merely natural transformations in a particular direction. We…

Let A be a finite alphabet and let L contained in (A*)^n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an…