Related papers: Logic Meets Algebra: the Case of Regular Languages
Reversible forms of computations are often interesting from an energy efficiency point of view. When the computation device in question is an automaton, it is known that the minimal reversible automaton recognizing a given language is not…
The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this…
The state complexity, respectively, nondeterministic state complexity of a regular language $L$ is the number of states of the minimal deterministic, respectively, of a minimal nondeterministic finite automaton for $L$. Some of the most…
Tractability results for the model checking problem of logics yield powerful algorithmic meta theorems of the form: Every computational problem expressible in a logic $L$ can be solved efficiently on every class $\mathscr{C}$ of structures…
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…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…
Both algebraic and computational approaches for dealing with similarity spaces are well known in generalized rough set theory. However, these studies may be said to have been confined to particular perspectives of distinguishability in the…
Floyd languages (FL), alias Operator Precedence Languages, have recently received renewed attention thanks to their closure properties and local parsability which allow one to apply automatic verification techniques (e.g. model checking)…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
We give an algebraic characterisation of first-order logic with the neighbour relation, on finite words. For this, we consider languages of finite words over alphabets with an involution on them. The natural algebras for such languages are…
The aim of this work is to develop a study from the perspective of Abstract Algebraic Logic of some bilattice-based logical systems introduced in the nineties by Ofer Arieli and Arnon Avron. The motivation for such an investigation has two…
Generalizations of numeration systems in which N is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language L over a finite alphabet A. For these systems, we obtain a…
Given an order of the underlying alphabet we can lift it to the states of a finite deterministic automaton: to compare states we use the order of the strings reaching them. When the order on strings is the co-lexicographic one \emph{and}…
We define a new class of languages of $\omega$-words, strictly extending $\omega$-regular languages. One way to present this new class is by a type of regular expressions. The new expressions are an extension of $\omega$-regular expressions…
We consider forkable regular expressions, which enrich regular expressions with a fork operator, to establish a formal basis for static and dynamic analysis of the communication behavior of concurrent programs. We define a novel…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…
Minimizing the size of finite automata is a fundamental problem in theoretical computer science. Beyond standard minimization, further reductions can be achieved by decomposing an automaton into smaller components whose languages combine…