Related papers: Categorical Liveness Checking by Corecursive Algeb…

Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…

Selective classification enables models to make predictions only when they are sufficiently confident, aiming to enhance safety and reliability, which is important in high-stakes scenarios. Previous methods mainly use deep neural networks…

A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…

Given a finite and non-empty set $X$ and randomly selected specific functions and relations on $X$, we investigate the existence and non-existence of fixed points and reflexive points, respectively. First, we consider the class of…

Nominal sets provide a framework to study key notions of syntax and semantics such as fresh names, variable binding and $\alpha$-equivalence on a conveniently abstract categorical level. Coalgebras for endofunctors on nominal sets model,…

In this article, we provide three coalgebraic characterizations of the class of context-free languages, each based on the idea of adding coalgebraic structure to an existing algebraic structure by specifying output-derivative pairs. Final…

This paper contributes to a theory of the behaviour of "finite-state" systems that is generic in the system type. We propose that such systems are modeled as coalgebras with a finitely generated carrier for an endofunctor on a locally…

Often fairness assumptions need to be made in order to establish liveness properties of distributed systems, but in many situations they lead to false conclusions. This document presents a research agenda aiming at laying the foundations of…

Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…

Every endofunctor of the category of classes is proved to be set-based in the sense of Aczel and Mendler, therefore, it has a final coalgebra. Other basic properties of these endofunctors are proved, e.g. the existence of a free completely…

We classify essential algebras whose irredundant non-refinable covers consist of primal algebras. The proof is obtained by constructing one to one correspondence between such algebras and partial orders on finite sets. Further, we prove…

Many machine learning algorithms rely on iterative updates of uncertainty representations, ranging from variational inference and expectation-maximization, to reinforcement learning, continual learning, and multi-agent learning. In the…

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 examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…

Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…

We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials as dynamical systems. This lays the foundation for classification results of more general classes of Newton maps. A fundamental…

We study the termination problem for nondeterministic recursive probabilistic programs. First, we show that a ranking-supermartingales-based approach is both sound and complete for bounded terminiation (i.e., bounded expected termination…

We describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries, over an algebraically closed field of characteristic zero.

Datasets can be biased due to societal inequities, human biases, under-representation of minorities, etc. Our goal is to certify that models produced by a learning algorithm are pointwise-robust to potential dataset biases. This is a…

While reasoning in a logic extending a complete Boolean basis is coNP-hard, restricting to conjunctive fragments of modal languages sometimes allows for tractable reasoning even in the presence of greatest fixpoints. One such example is the…