Towards a General Theory of Barbs, Contexts and Labels

Abstract

Abstract. Barbed bisimilarity is a widely-used behavioural equivalence for interactive systems: given a set of predicates (denoted "barbs", and representing basic observations on states) and a set of contexts (representing the possible execution environments), two systems are deemed to be equivalent if they verify the same barbs whenever inserted inside any of the chosen contexts. Despite its flexibility, this definition of equivalence is unsatisfactory, since often the quantification is over an infinite set of contexts, thus making barbed bisimilarity very hard to be verified.Should a labelled operational semantics be available for our system, more efficient observational equivalences might be adopted. To this end, a series of techniques have been proposed to derive labelled transition systems (LTSs) from unlabelled ones, the main example being Leifer and Milner's reactive systems. The underlying intuition is that labels are the "minimal" contexts that allow for a reduction to be performed.We introduce a framework that characterizes (weak) barbed bisimilarity via transition systems whose labels are (possibly minimal) contexts. Differently from other proposals, our theory is not dependent on the way LTSs are built, and it relies on a simple set-theoretical presentation. To provide a test-bed for our formalism, we instantiate it by addressing the semantics of mobile ambients and HoCore, recasting the (weak) barbed bisimilarities of these calculi via label-based behavioural equivalences.

A Behavioral Congruence for Concurrent Constraint Programming with Nondeterministic Choice

“…However, this condition does not capture the fact that in order to produce e, Q, true may have to evolve into a configuration which can no longer produce some of the weak barbs Q, true can produce. 7 Using this insight, we shall define a new notion of weak bisimilarity that changes condition (i) in≈ (Definition 9) in order to deal with the problem present in Figure 1. More concretely, condition (i) requires that whenever P, c ↓ α then Q, d ⇓ α , Q, d −→ * Q ′ , d ′ ↓ α without imposing any condition between P, c and Q ′ , d ′ .…”

“…This is not the case of ccp, where barbs are observations on the store, while labeled transitions are determined by the processes. A more abstract understanding of this peculiarity of ccp can be given within the framework of [7] which is an extension of [15] featuring barbs and weak semantics.…”

Barbed Semantics for Open Reactive Systems

“…So, it would be interesting to extend our framework by considering an automatically derived notion of barb for (open) GRSs. An alternate route would instead be to abstract away from the use of state predicates by providing an efficient labelled characterization of the barbed semantics, as shown for closed GRSs in [3,5].…”

“…The flexibility of the definition allows for recasting a variety of observational, bisimulation-based equivalences. Therefore, a suitable notion of barbed saturated semantics for RSs is introduced in [4], and it is further investigated in [3,5], where an efficient characterisation for both the strong and weak case is presented, avoiding to consider all contexts.…”