Abstract Trust is a multi-faceted phenomenon traditionally studied in human relations and more recently in human-machine interactions. In the context of AI-enabled systems, trust is about the belief of the user that in a given scenario the system is going to be helpful and safe. The system-side counterpart to trust is trustworthiness. When trust and trustworthiness are aligned with each other, there is calibrated trust. Trust, trustworthiness, and calibrated trust are all dynamic phenomena, evolving throughout the history and evolution of user beliefs, systems, and their interaction. In this paper, we review the basic concepts of trust, trustworthiness and calibrated trust and provide definitions for them. We discuss their various metrics used in the literature, and the causes that may affect their dynamics, particularly in the context of AI-enabled systems. We discuss the implications of the discussed concepts for various types of stakeholders and suggest some challenges for future research.

Abstract Automata learning is a technique to infer an automaton model of a black-box system via queries to the system. In recent years it has found widespread use both in industry and academia, as it enables formal verification when no model is available or it is too complex to create one manually. In this paper we consider the problem of learning the individual components of a black-box synchronous system, assuming we can only query the whole system. We introduce a compositional learning approach in which several learners cooperate, each aiming to learn one of the components. Our experiments show that, in many cases, our approach requires significantly fewer queries than a widely-used non-compositional algorithm such as $$\mathtt {L^*}$$ L ∗ .

We are motivated by the following question: which data languages admit an active learning algorithm? This question was left open in previous work by the authors, and is particularly challenging for languages recognised by nondeterministic automata. To answer it, we develop the theory of residual nominal automata, a subclass of nondeterministic nominal automata. We prove that this class has canonical representatives, which can always be constructed via a finite number of observations. This property enables active learning algorithms, and makes up for the fact that residuality -- a semantic property -- is undecidable for nominal automata. Our construction for canonical residual automata is based on a machine-independent characterisation of residual languages, for which we develop new results in nominal lattice theory. Studying residuality in the context of nominal languages is a step towards a better understanding of learnability of automata with some sort of nondeterminism.

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 by and resembles the standard breadth-first search procedure to compute the reachable part of a graph. We also study coalgebras in Kleisli categories: for a functor extending a functor on the base category, we show that the reachable part of a given pointed coalgebra can be computed in that base category.

Symbolic Finite Automata and Register Automata are two orthogonal extensions of finite automata motivated by real-world problems where data may have unbounded domains. These automata address a demand for a model over large or infinite alphabets, respectively. Both automata models have interesting applications and have been successful in their own right. In this paper, we introduce Symbolic Register Automata, a new model that combines features from both symbolic and register automata, with a view on applications that were previously out of reach. We study their properties and provide algorithms for emptiness, inclusion and equivalence checking, together with experimental results.

Replicated Data Types (RDTs) have been introduced as a suitable abstraction for dealing with weakly consistent data stores, which may (temporarily) expose multiple, inconsistent views of their state. In the literature, RDTs are commonly specified in terms of two relations: visibility, which accounts for the different views that a store may have, and arbitration, which states the logical order imposed on the operations executed over the store. Different flavours, e.g., operational, axiomatic and functional, have recently been proposed for the specification of RDTs. In this work, we propose an algebraic characterisation of RDT specifications. We define categories of visibility relations and arbitrations, show the existence of relevant limits and colimits, and characterize RDT specifications as functors between such categories that preserve these additional structures.

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 have to be developed from scratch because there was no abstract theory offering guidelines. This makes it hard to devise such algorithms, and it obscures their correctness proofs. We introduce a simple category-theoretic formalism that provides an appropriately abstract foundation for studying automata learning. Furthermore, our framework establishes formal relations between algorithms for learning, testing, and minimization. We illustrate its generality with two examples: deterministic and weighted automata.

We present an Angluin-style algorithm to learn nominal automata, which are acceptors of languages over infinite (structured) alphabets. The abstract approach we take allows us to seamlessly extend known variations of the algorithm to this new setting. In particular we can learn a subclass of nominal non-deterministic automata. An implementation using a recently developed Haskell library for nominal computation is provided for preliminary experiments.