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Coalgebraic Behavioral Metrics

Paolo Baldan ; Filippo Bonchi ; Henning Kerstan ; Barbara König.

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 a framework for deriving pseudometrics on $X$ which measure&nbsp;[&hellip;]

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Convexity via Weak Distributive Laws

Filippo Bonchi ; Alessio Santamaria.

We study the canonical weak distributive law $\delta$ of the powerset monad over the semimodule monad for a certain class of semirings containing, in particular, positive semifields. For this subclass we characterise $\delta$ as a convex closure in the free semimodule of a set. Using the abstract&nbsp;[&hellip;]

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The Theory of Traces for Systems with Nondeterminism, Probability, and Termination

Filippo Bonchi ; Ana Sokolova ; Valeria Vignudelli.

This paper studies trace-based equivalences for systems combining nondeterministic and probabilistic choices. We show how trace semantics for such processes can be recovered by instantiating a coalgebraic construction known as the generalised powerset construction. We characterise and compare the&nbsp;[&hellip;]

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