Weak bisimulations for the Giry monad

Doberkat, Ernst–Erich

doi:10.1017/s0960129510000204

Cited by 1 publication

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“…Some follow Milner's "double arrow" construction (i.e., strong bisimulations of the system saturated under τ -transitions), but in general this construction does not work; in particular for quantitative systems we cannot apply directly this schema, and many other solutions have been proposed; see e.g. [7,47,6,31,18,12]. In non-deterministic probabilistic systems, for example, the counterpart of Milner's weak bisimulation is Segala's weak bisimulation [43], which differs from Baier-Hermann's [5].…”

Section: Introductionmentioning

confidence: 99%

Behavioural equivalences for coalgebras with unobservable moves

Brengos

Miculan

Peressotti

2015

Journal of Logical and Algebraic Methods in Programming

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We introduce a general categorical framework for the definition of weak behavioural equivalences, building on and extending recent results in the field. This framework is based on special order enriched categories, i.e. categories whose homsets are endowed with suitable complete orders. Using this structure we provide an abstract notion of saturation, which allows us to define various (weak) behavioural equivalences. We show that the Kleisli categories of many common monads are categories of this kind. On one hand, this allows us to instantiate the abstract definitions to a wide range of existing systems (weighted LTS, Segala systems, calculi with names, etc.), recovering the corresponding notions of weak behavioural equivalences; on the other, we can readily provide new weak behavioural equivalences for more complex behaviours, like those definable on presheaves, topological spaces, measurable spaces, etc.

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