176 research outputs found
Bisimulation maps in presheaf categories
The category of presheaves on a (small) category is a suitable semantic universe to study behaviour of various dynamical systems. In particular, presheaves can be used to record the executions of a system and their morphisms correspond to simulation maps for various kinds of state-based systems. In this paper, we introduce a notion of bisimulation maps between presheaves (or executions) to capture well known behavioural equivalences in an abstract way. We demonstrate the versatility of this framework by working out the characterisations for standard bisimulation, ∀-fair bisimulation, and branching bisimulation
On path-based coalgebras and weak notions of bisimulation
It is well known that the theory of coalgebras provides an abstract definition of behavioural equivalence that coincides with strong bisimulation across a wide variety of state-based systems. Unfortunately, the theory in the presence of so-called silent actions is not yet fully developed. In this paper, we give a coalgebraic characterisation of branching (delay) bisimulation in the context of labelled transition systems (fully probabilistic systems). It is shown that recording executions (up to a notion of stuttering), rather than the set of successor states, from a state is sufficient to characterise the respected bisimulation relations in both cases
A coalgebraic semantics for causality in Petri nets
In this paper we revisit some pioneering efforts to equip Petri nets with
compact operational models for expressing causality. The models we propose have
a bisimilarity relation and a minimal representative for each equivalence
class, and they can be fully explained as coalgebras on a presheaf category on
an index category of partial orders. First, we provide a set-theoretic model in
the form of a a causal case graph, that is a labeled transition system where
states and transitions represent markings and firings of the net, respectively,
and are equipped with causal information. Most importantly, each state has a
poset representing causal dependencies among past events. Our first result
shows the correspondence with behavior structure semantics as proposed by
Trakhtenbrot and Rabinovich. Causal case graphs may be infinitely-branching and
have infinitely many states, but we show how they can be refined to get an
equivalent finitely-branching model. In it, states are equipped with
symmetries, which are essential for the existence of a minimal, often
finite-state, model. The next step is constructing a coalgebraic model. We
exploit the fact that events can be represented as names, and event generation
as name generation. Thus we can apply the Fiore-Turi framework: we model causal
relations as a suitable category of posets with action labels, and generation
of new events with causal dependencies as an endofunctor on this category. Then
we define a well-behaved category of coalgebras. Our coalgebraic model is still
infinite-state, but we exploit the equivalence between coalgebras over a class
of presheaves and History Dependent automata to derive a compact
representation, which is equivalent to our set-theoretical compact model.
Remarkably, state reduction is automatically performed along the equivalence.Comment: Accepted by Journal of Logical and Algebraic Methods in Programmin
Full abstraction for fair testing in CCS (expanded version)
In previous work with Pous, we defined a semantics for CCS which may both be
viewed as an innocent form of presheaf semantics and as a concurrent form of
game semantics. We define in this setting an analogue of fair testing
equivalence, which we prove fully abstract w.r.t. standard fair testing
equivalence. The proof relies on a new algebraic notion called playground,
which represents the `rule of the game'. From any playground, we derive two
languages equipped with labelled transition systems, as well as a strong,
functional bisimulation between them.Comment: 80 page
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