Related papers: Behavioural Metrics: Compositionality of the Kanto…
Behavioural distances measure the deviation between states in quantitative systems, such as probabilistic or weighted systems. There is growing interest in generic approaches to behavioural distances. In particular, coalgebraic methods…
The Kantorovich distance is a widely used metric between probability distributions. The Kantorovich-Rubinstein duality states that it can be defined in two equivalent ways: as a supremum, based on non-expansive functions into [0, 1], and as…
Up-to techniques are a well-known method for enhancing coinductive proofs of behavioural equivalences. We introduce up-to techniques for behavioural metrics between systems modelled as coalgebras and we provide abstract results to prove…
We study behavioral metrics in an abstract coalgebraic setting. Given a coalgebra alpha: X -> FX in Set, where the functor F specifies the branching type, we define a framework for deriving pseudometrics on X which measure the behavioral…
We study different behavioral metrics, such as those arising from both branching and linear-time semantics, in a coalgebraic setting. Given a coalgebra $\alpha\colon X \to HX$ for a functor $H \colon \mathrm{Set}\to \mathrm{Set}$, we define…
While behavioural equivalences among systems of the same type, such as Park/Milner bisimilarity of labelled transition systems, are an established notion, a systematic treatment of relationships between systems of different type is…
Many behavioural equivalences or preorders for probabilistic processes involve a lifting operation that turns a relation on states into a relation on distributions of states. We show that several existing proposals for lifting relations can…
The classical Kantorovich-Rubinstein duality guarantees coincidence between metrics on the space of probability distributions defined on the one hand via transport plans (couplings) and on the other hand via price functions. Both…
Proving compositionality of behavioral equivalence on state-based systems with respect to algebraic operations is a classical and widely studied problem. We study a categorical formulation of this problem, where operations on state-based…
The most studied and accepted pseudometric for probabilistic processes is one based on the Kantorovich distance between distributions. It comes with many theoretical and motivating results, in particular it is the fixpoint of a given…
Functor lifting along a fibration is used for several different purposes in computer science. In the theory of coalgebras, it is used to define coinductive predicates, such as simulation preorder and bisimilarity. Codensity lifting is a…
Up-to techniques' represent enhancements of the coinduction proof method and are widely used on coinductive behavioural relations such as bisimilarity. Abstract formulations of these coinductive techniques exist, using fixed-points or…
The analysis and control of stochastic dynamical systems rely on probabilistic models such as (continuous-space) Markov decision processes, but large or continuous state spaces make exact analysis intractable and call for principled…
We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the…
We introduce an adaptive refinement procedure for smart, and scalable abstraction of dynamical systems. Our technique relies on partitioning the state space depending on the observation of future outputs. However, this knowledge is…
Behavioural conformances -- e.g. behavioural equivalences, distances, preorders -- on a wide range of system types (non-deterministic, probabilistic, weighted etc.) can be dealt with uniformly in the paradigm of universal coalgebra. One of…
In this paper we show how the abstract behaviours of higher-order systems can be modelled as final coalgebras of suitable behavioural functors. These functors have the challenging peculiarity to be circularly defined with their own final…
We introduce and study the class of linear transfers between probability distributions and the dual class of Kantorovich operators between function spaces. Linear transfers can be seen as an extension of convex lower semi-continuous…
In this paper we propose two behavioral distances that support approximate reasoning on Stochastic Markov Models (SMMs), that are continuous-time stochastic transition systems where the residence time on each state is described by a generic…
The classical Hennessy-Milner theorem is an important tool in the analysis of concurrent processes; it guarantees that any two non-bisimilar states in finitely branching labelled transition systems can be distinguished by a modal formula.…