Related papers: A Categorical Approach to Syntactic Monoids
Let $R$ be a regular ring of dimension $d$ and $L$ be a $c$-divisible monoid. If ${K}_1{Sp}(R)$ is trivial and $k \geq d+2,$ then we prove that the symplectic group ${Sp}_{2k}(R[L])$ is generated by elementary symplectic matrices over…
A group is Markov if it admits a prefix-closed regular language of unique representatives with respect to some generating set, and strongly Markov if it admits such a language of unique minimal-length representatives over every generating…
Krebs et al. (2007) gave a characterization of the complexity class TC0 as the class of languages recognized by a certain class of typed monoids. The notion of typed monoid was introduced to extend methods of algebraic automata theory to…
In this paper we continue a classical work of Sch\"utzenberger on codes with bounded synchronization delay. He was interested to characterize those regular languages where the groups in the syntactic monoid belong to a variety $H$. He…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
We construct certain monoids, called tied monoids. These monoids result to be semidirect products finitely presented and commonly built from braid groups and their relatives acting on monoids of set partitions. The nature of our monoids…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
This paper investigates the use of symmetric monoidal closed (SMC) structure for representing syntax with variable binding, in particular for languages with linear aspects. In our setting, one first specifies an SMC theory T, which may…
In this technical report we describe a general class of monoids for which (sub)sequential rational can be characterised in terms of a congruence relation in the flavour of Myhill-Nerode relation. The class of monoids that we consider can be…
We study the variety ZG of monoids where the elements that belong to a group are central, i.e., commute with all other elements. We show that ZG is local, that is, the semidirect product ZG * D of ZG by definite semigroups is equal to LZG,…
While a language assigns a value of either `yes' or `no' to each word, a lattice language assigns an element of a given lattice to each word. An advantage of lattice languages is that joins and meets of languages can be defined as…
Algebraic theories, sometimes called equational theories, are syntactic notions given by finitary operations and equations, such as monoids, groups, and rings. There is a well-known category-theoretic treatment of them that algebraic…
We consider a set of natural operations on languages, and prove that the orbit of any language L under the monoid generated by this set is finite and bounded, independently of L. This generalizes previous results about complement, Kleene…
The free monoid $A^*$ on a finite totally ordered alphabet $A$ acts at the left on columns, by Schensted left insertion. This defines a finite monoid, denoted $Styl(A)$ and called the stylic monoid. It is canonically a quotient of the…
We study a model of one-way quantum automaton where only measurement operations are allowed ($\mon$). We give an algebraic characterization of $\lmo(\Sigma)$, showing that the syntactic monoids of the languages in $\lmo(\Sigma)$ are exactly…
We develop an effective and natural approach to interpret any semigroup admitting a special language of greedy normal forms as an automaton semigroup,namely the semigroup generated by a Mealy automaton encoding the behaviour of such a…
One of the main reasons for the correspondence of regular languages and monadic second-order logic is that the class of regular languages is closed under images of surjective letter-to-letter homomorphisms. This closure property holds for…
We prove several results concerning finitely generated submonoids of the free monoid. These results generalize those known for free submonoids. We prove in particular that if $X=Y\circ Z$ is a composition of finite sets of words with $Y$…
For every fixed class of regular languages, there is a natural hierarchy of increasingly more general problems: Firstly, the membership problem asks whether a given language belongs to the fixed class of languages. Secondly, the separation…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…