Related papers: Syntactic Structures of Regular Languages

Matching Logic is a framework for specifying programming language semantics and reasoning about programs. Its formulas are called patterns and are built with variables, symbols, connectives and quantifiers. A pattern is a combination of…

A new language model for speech recognition is presented. The model develops hidden hierarchical syntactic-like structure incrementally and uses it to extract meaningful information from the word history, thus complementing the locality of…

In this paper, we use a categorical and functorial set up to model the syntax and inference of logics with algebraic signature, extending previous works on algebraisation of logics. The main feature of this work is that structurality, or…

We deal with equations over free semilattice of infinite rank and prove that any infinite consistent system of equations is equivalent to its finite subsystem. Moreover, we describe irreducible algebraic sets and solve some algorithmic…

Syntactic language models (SLMs) enhance Transformers by incorporating syntactic biases through the modeling of linearized syntactic parse trees alongside surface sentences. This paper focuses on compositional SLMs that are based on…

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…

We introduce regular languages of morphisms in free monoidal categories, with their associated grammars and automata. These subsume the classical theory of regular languages of words and trees, but also open up a much wider class of…

The paper presents a language model that develops syntactic structure and uses it to extract meaningful information from the word history, thus enabling the use of long distance dependencies. The model assigns probability to every joint…

The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…

Syntactic discontinuity is a grammatical phenomenon in which a constituent is split into more than one part because of the insertion of an element which is not part of the constituent. This is observed in many languages across the world…

The correspondence between monoidal categories and graphical languages of diagrams has been studied extensively, leading to applications in quantum computing and communication, systems theory, circuit design and more. From the categorical…

Every metric symplectic Lie algebra has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding quadratic cohomology sets. Finally, we give a scheme to classify the…

Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…

The binary products of right, left or double division in semigroups that are semilattices of groups give interesting groupoid structures that are in one to one correspondence with semigroups that are semilattices of groups. This work is…

A natural next step in the evolution of constraint-based grammar formalisms from rewriting formalisms is to abstract fully away from the details of the grammar mechanism---to express syntactic theories purely in terms of the properties of…

In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models…

We define a class of associative algebras generalizing 'clannish algebras', as introduced by the second author, but also incorporating semilinear structure, like a skew polynomial ring. Clannish algebras generalize the well known 'string…

We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…

We introduce the concept of a consistency space. The idea of the consistency space is motivated by the question, Given only the collection of sets of sentences which are logically consistent, is it possible to reconstruct their lattice…

In this paper we study the lattice of restricted subalgebras of a restricted Lie algebra. In particular, we consider those algebras in which this lattice is dually atomistic, lower or upper semimodular, or in which every restricted…