Related papers: Non-Deterministic Kleene Coalgebras
Operational semantics have been enormously successful, in large part due to its flexibility and simplicity, but they are not compositional. Denotational semantics, on the other hand, are compositional but the lattice-theoretic models are…
The development of mechanised language specification based on structured operational semantics, with applications to verified compilers and sound program analysis, requires huge effort. General theory and frameworks have been proposed to…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
Non-deterministic Finite Automata (NFA) represent regular languages concisely, increasing their appeal for applications such as word recognition. This paper proposes a new approach to generate NFA from an interaction language such as UML…
We introduce Probabilistic Guarded Kleene Algebra with Tests (ProbGKAT), an extension of GKAT that allows reasoning about uninterpreted imperative programs with probabilistic branching. We give its operational semantics in terms of special…
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…
The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration…
Coalgebras provide a uniform framework to study dynamical systems, including several types of automata. In this paper, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are…
We show that the commutative closure combined with the iterated shuffle is a regularity-preserving operation on group languages. In particular, for commutative group languages, the iterated shuffle is a regularity-preserving operation. We…
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 investigate the expressive power of regular expressions for languages of countable words and establish their expressive equivalence with logical and algebraic characterizations. Our goal is to extend the classical theory of regular…
We study counting-regular languages -- these are languages $L$ for which there is a regular language $L'$ such that the number of strings of length $n$ in $L$ and $L'$ are the same for all $n$. We show that the languages accepted by…
In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and…
Large Language Models (LLMs) have become capable of generating highly fluent text in certain languages, without modules specially designed to capture grammar or semantic coherence. What does this mean for the future of linguistic expertise…
The aim of this paper is to design the polynomial construction of a finite recognizer for hairpin completions of regular languages. This is achieved by considering completions as new expression operators and by applying derivation…
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…
Synchronous Kleene algebra (SKA), an extension of Kleene algebra (KA), was proposed by Prisacariu as a tool for reasoning about programs that may execute synchronously, i.e., in lock-step. We provide a countermodel witnessing that the…
Cayley graphs have a number of useful features: the ability to graphically represent finitely generated group elements and their relations; to name all vertices relative to a point; and the fact that they have a well-defined notion of…
We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
Neural network models often generalize poorly to mismatched domains or distributions. In NLP, this issue arises in particular when models are expected to generalize compositionally, that is, to novel combinations of familiar words and…