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Neuro-symbolic reasoning increasingly demands frameworks that unite the formal rigor of logic with the interpretability of large language models (LLMs). We introduce an end to end explainability by construction pipeline integrating the…
In this thesis we use quasiorders on words to offer a new perspective on two well-studied problems from Formal Language Theory: deciding language inclusion and manipulating the finite automata representations of regular languages. First, we…
The class of Boolean combinations of tree languages recognized by deterministic top-down tree automata (also known as deterministic root-to-frontier automata) is studied. The problem of determining for a given regular tree language whether…
We give a presentation theorem for continuous first-order logic and Metric Abstract Elementary classes in terms of $L_{\omega_1, \omega}$ and Abstract Elementary Classes, respectively. This presentation is accomplished by analyzing dense…
We provide an extension of concurrent Kleene algebras to account for probabilistic properties. The algebra yields a unified framework containing nondeterminism, concurrency and probability and is sound with respect to the set of…
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 present a generalizable classification approach that leverages Large Language Models (LLMs) to facilitate the detection of implicitly encoded social meaning in conversations. We design a multi-faceted prompt to extract a textual…
A condition characterizing the class of regular languages which have several nonisomorphic minimal reversible automata is presented. The condition concerns the structure of the minimum automaton accepting the language under consideration.…
Over the past decades, coordination languages have emerged for the specification and implementation of interaction protocols for communicating software components. This class of languages includes Reo, a platform for compositional…
Language models and conversational systems are growing increasingly advanced, creating outputs that may be mistaken for humans. Consumers may thus be misled by advertising, media reports, or vagueness regarding the role of automation in the…
Operator precedence grammars define a classical Boolean and deterministic context-free family (called Floyd languages or FLs). FLs have been shown to strictly include the well-known visibly pushdown languages, and enjoy the same nice…
The Sigma formulas of the language of arithmetic express semidecidable relations on the natural numbers. More generally, whenever a totality of objects is regarded as incomplete, the Sigma formulas express relations that are witnessed in a…
We study subsystems of open induction which are strongly connected to methods of automated inductive theorem proving. Specifically, we consider systems obtained from restricting induction to atoms, literals, clauses, and dual clauses. We…
Large language models (LLMs) demonstrate exceptional performance on tasks requiring complex linguistic abilities, such as reference disambiguation and metaphor recognition/generation. Although LLMs possess impressive capabilities, their…
In the present paper, we introduce a multi-type calculus for the logic of measurable Kleene algebras, for which we prove soundness, completeness, conservativity, cut elimination and subformula property. Our proposal imports ideas and…
We explore language semantics for automata combining probabilistic and nondeterministic behavior. We first show that there are precisely two natural semantics for probabilistic automata with nondeterminism. For both choices, we show that…
Regular nested word languages (a.k.a. visibly pushdown languages) strictly extend regular word languages, while preserving their main closure and decidability properties. Previous works have shown that considering languages of 2-nested…
Following a seminar the present author gave to an Automata Theory course to computer science students, it will be presented, in a very synthetic and mostly selfcontained way, the principal properties of context free languages (CFL), with…
This thesis explores how concepts of formal language theory can be used to study left-orderable groups. It analyses the languages formed by their positive cones and demonstrates how the abstract families of languages (AFLs) in the Chomsky…
Automata operating on strings of nested brackets, known as input-driven pushdown automata, and as visibly pushdown automata, have been studied since the 1980s. They were extended to the case of infinite strings by Alur and Madhusudan…