Related papers: Deque languages, automata and planar graphs

We define compact automata and show that every language has a unique minimal compact automaton. We also define recognition of languages by compact left semitopological monoids and construct the analogue of the syntactic monoid in this…

This paper presents three case studies of modeling aspects of lexical processing with Linear Discriminative Learning (LDL), the computational engine of the Discriminative Lexicon model (Baayen et al., 2019). With numeric representations of…

It is well known that the "store language" of every pushdown automaton -- the set of store configurations (state and stack contents) that can appear as an intermediate step in accepting computations -- is a regular language. Here many…

Current generative knowledge graph construction approaches usually fail to capture structural knowledge by simply flattening natural language into serialized texts or a specification language. However, large generative language model…

Large language models (LLMs) have significantly advanced performance across a spectrum of natural language processing (NLP) tasks. Yet, their application to knowledge graphs (KGs), which describe facts in the form of triplets and allow…

In a one-counter automaton (OCA), one can produce a letter from some finite alphabet, increment and decrement the counter by one, or compare it with constants up to some threshold. It is well-known that universality and language inclusion…

It is an open problem to characterize the class of languages recognized by quantum finite automata (QFA). We examine some necessary and some sufficient conditions for a (regular) language to be recognizable by a QFA. For a subclass of…

Table understanding requires structured, multi-step reasoning. Large Language Models (LLMs) struggle with it due to the structural complexity of tabular data. Recently, multi-agent frameworks for SQL generation have shown promise in…

Human syntactic structures are usually represented as graphs. Much research has focused on the mapping between such graphs and linguistic sequences, but less attention has been paid to the shapes of the graphs themselves: their topologies.…

Let D denote an infinite alphabet -- a set that consists of infinitely many symbols. A word w = a_0 b_0 a_1 b_1 ... a_n b_n of even length over D can be viewed as a directed graph G_w whose vertices are the symbols that appear in w, and the…

Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. In this paper, we provide a theoretical basis for querying categorical databases. We…

We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…

Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes,…

Higher-dimensional automata (HDA) are a model of concurrency that models simultaneous execution of events using higher dimensional cells. HDA recognize languages of pomsets, a generalization of finite words whose letters are partially…

In this paper we develop little further the theory of quantum finite automata (QFA). There are already few properties of QFA known, that deterministic and probabilistic finite automata do not have e.g. they cannot recognize all regular…

The design of asynchronous circuits typically requires a judicious definition of signals and modules, combined with a proper specification of their timing constraints, which can be a complex and error-prone process, using standard Hardware…

The states of a deterministic finite automaton A can be identified with collections of words in Pf(L(A)) -- the set of prefixes of words belonging to the regular language accepted by A. But words can be ordered and among the many possible…

This paper proposes a connection method \`a la Bibel for an exception-tolerant family of description logics (DLs). As for the language, we assume the DL $\mathcal{ALCH}$ extended with two typicality operators: one on (complex) concepts and…

Analytics on structured data is a mature field with many successful methods. However, most real world data exists in unstructured form, such as images and conversations. We investigate the potential of Large Language Models (LLMs) to enable…

We define a class of languages of infinite words over infinite alphabets, and the corresponding automata. The automata used for recognition are a generalisation of deterministic Muller automata to the setting of nominal sets. Remarkably,…