Related papers: Generalizing determinization from automata to coal…
Automata learning is a technique that has successfully been applied in verification, with the automaton type varying depending on the application domain. Adaptations of automata learning algorithms for increasingly complex types of automata…
These lecture notes are intended as a supplement to Moore and Mertens' The Nature of Computation or as a standalone resource, and are available to anyone who wants to use them. Comments are welcome, and please let me know if you use these…
Compositional generalization is the ability to generalize systematically to a new data distribution by combining known components. Although humans seem to have a great ability to generalize compositionally, state-of-the-art neural models…
Nominal automata models serve as a formalism for data languages, and in fact often relate closely to classical register models. The paradigm of name allocation in nominal automata helps alleviate the pervasive computational hardness of…
Recent works have shown that defining a behavioural equivalence that matches the observational properties of a quantum-capable, concurrent, non-deterministic system is a surprisingly difficult task. We explore coalgebras over distributions…
A coalgebraic definition of finite and infinite trace semantics for probabilistic transition systems has recently been given using a certain Kleisli category. In this paper this semantics is developed using a coalgebraic method which is an…
Probabilistic automata (PA), also known as probabilistic nondeterministic labelled transition systems, combine probability and nondeterminism. They can be given different semantics, like strong bisimilarity, convex bisimilarity, or (more…
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,…
Compositional generalization is a basic and essential intellective capability of human beings, which allows us to recombine known parts readily. However, existing neural network based models have been proven to be extremely deficient in…
The paper gives an example of a tree language G that is recognised by an unambiguous parity automaton and is analytic-complete as a set in Cantor space. This already shows that the unambiguous languages are topologically more complex than…
Many methods for the verification of complex computer systems require the existence of a tractable mathematical abstraction of the system, often in the form of an automaton. In reality, however, such a model is hard to come up with, in…
In previous work, categories of algebras of endofunctors were shown to be enriched in categories of coalgebras of the same endofunctor, and the extra structure of that enrichment was used to define a generalization of inductive data types.…
The article defines and studies the genus of finite state deterministic automata (FSA) and regular languages. Indeed, a FSA can be seen as a graph for which the notion of genus arises. At the same time, a FSA has a semantics via its…
The extent to which neural networks are able to acquire and represent symbolic rules remains a key topic of research and debate. Much current work focuses on the impressive capabilities of large language models, as well as their often…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have…
Coalgebras for an endofunctor provide a category-theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired…
We present positive coalgebraic logic in full generality, and show how to obtain a positive coalgebraic logic from a boolean one. On the model side this involves canonically computing an endofunctor $T': Pos\to Pos$ from an endofunctor $T:…
The transformation of a nondeterministic finite-state automaton into a deterministic finite-state automaton is an integral part of any course on formal languages and automata theory. For some students, understanding this transformation is…
We use dialgebras, generalising both algebras and coalgebras, as a complement of the standard coalgebraic framework, aimed at describing the semantics of an interactive system by the means of reaction rules. In this model, interaction is…