Adequacy Issues in Reactive Systems: Barbed Semantics for Mobile Ambients

Reactive systems represent a meta-framework aimed at deriving behavioral congruences for those specification formalisms whose operational semantics is provided by rewriting rules. The aim of this thesis is to address one of the main issues of the framework, concerning the adequacy of the standard observational semantics (the IPO and the saturated one) in modelling the concrete semantics of actual formalisms. The problem is that IPO-bisimilarity (obtained considering only minimal labels) is often too discriminating, while the saturated one (via all labels) may be too coarse, and intermediate proposals should then be put forward. We then introduce a more expressive semantics for reactive systems which, thanks to its flexibility, allows for recasting a wide variety of observational, bisimulation-based equivalences. In particular, we propose suitable notions of barbed and weak barbed semantics for reactive systems, and an efficient characterization of them through the IPO-transition systems. We also propose a novel, more general behavioural equivalence: L-bisimilarity, which is able to recast both its IPO and saturated counterparts, as well as the barbed one. The equivalence is parametric with respect to a set L of reactive systems labels, and it is shown that under mild conditions on L it is a congruence. In order to provide a suitable test-bed, we instantiate our proposal over the asynchronous CCS and, most importantly, over the mobile ambients calculus, whose semantics is still in a flux

On Barbs and Labels in Reactive Systems

Reactive systems (RSs) represent a meta-framework aimed at deriving behavioral congruences for those computational formalisms whose operational semantics is provided by reduction rules. RSs proved a flexible specification device, yet so far most of the efforts dealing with their behavioural semantics focused on idem pushouts (IPOs) and saturated (also known as dynamic) bisimulations. In this paper we introduce a novel, intermediate behavioural equivalence: L-bisimilarity, which is able to recast both its IPO and saturated counterparts. The equivalence is parametric with respect to a set L of RSs labels, and it is shown that under mild conditions on L it is indeed a congruence. Furthermore, L-bisimilarity can also recast the notion of barbed semantics for RSs, proposed by the same authors in a previous paper. In order to provide a suitable test-bed, we instantiate our proposal by addressing the semantics of (asynchronous) CCS and of the calculus of mobile ambients

A Decentralized Implementation Of Mobile Ambients

We present a graphical implementation for finite processes of the mobile ambients calculus. Our encoding uses unstructured (i.e., non hierarchical) graphs and it is sound and complete with respect to the structural congruence of the calculus (that is, two processes are equivalent iff they are mapped into isomorphic graphs). With respect to alternative proposals for the graphical implementation of mobile ambients, our encoding distinguishes the syntactic structure of a process from the activation order of a process components. Our solution faithfully captures a basic feature of the calculus (ambients can be nested and reductions are propagated across ambient nesting) and it allows to model the reduction semantics via a graph transformation system containing just three rules

Labeled Transitions for Mobile Ambients

The paper presents a case study on the synthesis of labelled transition systems (LTSs) for process calculi, choosing as testbed Cardelli and Gordon's Mobile Ambients (MAs). The proposal is based on a graphical encoding: each process is mapped into a graph equipped with suitable interfaces, such that the denotation is fully abstract with respect to the usual structural congruence. Graphs with interfaces are amenable to the synthesis mechanism proposed by Ehrig and Koenig and based on borrowed contexts (BCs), an instance of relative pushouts, introduced by Leifer and Milner. The BC mechanism allows the effective construction of a LTS that has graphs with interfaces as both states and labels, and such that the associated bisimilarity is automatically a congruence. Our paper focuses on the analysis of a LTS over (processes as) graphs with interfaces, as distilled by exploiting the graphical encoding of MAs. In particular, we use the LTS on graphs to recover a suitable LTS directly defined over the structure of MAs processes

RPO semantics for Mobile Ambients

The paper focuses on the synthesis of labelled transition systems (LTSs) for process calculi, choosing as testbed Mobile Ambients (MAs). The proposal is based on a graphical encoding: a process is mapped into a graph equipped with interfaces, such that the denotation is fully abstract with respect to the standard structural congruence. Graphs with interfaces are amenable to the synthesis mechanism based on borrowed contexts (BCs), an instance of relative pushouts (RPOs). The BC mechanism allows the effective construction of an LTS that has graphs with interfaces as states and labels, and such that the associated bisimilarity is a congruence. Our paper focuses on the analysis of an LTS over processes as graphs with interfaces: we use the LTS on graphs to recover an LTS directly defined over the structure of MAs processes, further defining a set of SOS inference rules capturing the same operational semantics

Towards a General Theory of Barbs, Contexts and Labels

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

Labelled Transitions for Mobile Ambients (As Synthesized via a Graphical Encoding)

The paper presents a case study on the synthesis of labelled transition systems (LTSs) for process calculi, choosing as testbed Cardelli and Gordon’s Mobile Ambients (MAs). The proposal is based on a graphical encoding: each process is mapped into a graph equipped with suitable interfaces, such that the denotation is fully abstract with respect to the usual structural congruence. Graphs with interfaces are amenable to the synthesis mechanism proposed by Ehrig and König and based on borrowed contexts (BCs), an instance of relative pushouts, introduced by Leifer and Milner. The BC mechanism allows the effective construction of a LTS that has graphs with interfaces as both states and labels, and such that the associated bisimilarity is automatically a congruence. Our paper focuses on the analysis of a LTS over (processes as) graphs with interfaces, as distilled by exploiting the graphical encoding of MAs. In particular, we use the LTS on graphs to recover a suitable LTS directly defined over the structure of MAs processes

Encoding synchronous interactions using labelled Petri nets

We present an encoding of (bound) CSP processes with replication into Petri nets with labelled transitions. Through the encoding, the firing semantics of Petri nets models the standard operational semantics of CSP processes, which is both preserved and reflected. This correspondence allows for describing by net semantics the standard CSP observational equivalences. Since the encoding is modular with respect to process syntax, the paper puts on a firm ground the technology transfer between the two formalisms, e.g. recasting into the CSP framework well-established results like decidability of coverability for nets. This work complements previous results concerning the encoding of asynchronous interactions, thus witnessing the expressiveness of (open) labelled nets in modelling process calculi with alternative communication patterns