On the Expressiveness of Pure Mobile Ambients

We consider the Pure Ambient Calculus, which is Cardelli and Gordon's Ambient Calculus (or more precisely its safe version by Levi and Sangiorgi) restricted to its mobility primitives, and we focus on its expressive power. Since it has no form of communication or substitution, we show how these notions can be simulated by mobility and modifications in the hierarchical structure of ambients. As an example, we give an encoding of the synchronous π-calculus into pure ambients and we state an operational correspondence result. In order to simplify the proof and give an intuitive understanding of the encoding, we design an intermediate language: the π-Calculus with Explicit Substitutions and Channels, which is a syntactic extension of the π-calculus with a specific operational semantics.     

Ambient Petri Nets

Both the Ambient Calculus by L. Cardelli and the Elementary Object Systems by R. Valk model the behaviour of mobile systems. The Ambient Calculus is based on the concept of ambient, which is an environment with a given name that is delimited by a boundary, where some internal processes are executed. The main property of these ambients is that they can be moved to a new location thus modeling mobility. Elementary Object Systems are two-level net systems composed of a system net and one or more object nets, which can be seen as high-level token objects of the system net modeling the execution of mobile processes. This paper intends to contribute to the relationship between both frameworks by defining a multilevel extension of Elementary Object Systems, which will be used to provide a denotational semantics of a new process algebra called APBC (Ambient Petri Box Calculus). Such process algebra is an extension of the Petri Box Calculus that includes both ambients and their mobility capabilities, which conversely can be also interpreted as an extension of the Ambient Calculus with the main operations from the PBC.     

Encoding Distributed Areas and Local Communication into the π-Calculus

We show how the π-calculus can express local communications within a distributed system, through an encoding of the local area π-calculus, an enriched system that explicitly represents names which are known universally but always refer to local information. Our translation replaces point-to-point communication with a system of shared local ethers; we prove that this preserves and reflects process behaviour. We give an example based on an internet service dæmon, and investigate some limitations of the encoding.     

Parametric synchronizations in mobile nominal calculi

We present and compare P-PRISMA and F-PRISMA, two parametric calculi that can be instantiated with different interaction policies, defined as synchronization algebras with mobility of names (SAMs). In particular, P-PRISMA is based on name transmission (P-SAM), like π-calculus, and thus exploits directional (input–output) communication only, while F-PRISMA is based on name fusion (F-SAM), like Fusion calculus, and thus exploits a more symmetric form of communication. However, P-PRISMA and F-PRISMA can easily accommodate many other high-level synchronization mechanisms than the basic ones available in π-calculus and Fusion, hence allowing for the development of a general meta-theory of mobile calculi. We define for both the labeled operational semantics and a form of strong bisimilarity, showing that the latter is compositional for any SAM. We also discuss reduction semantics and weak bisimilarity. We give several examples based on heterogeneous SAMs, we investigate the case studies of π-calculus and Fusion calculus giving correspondence theorems, and we show how P-PRISMA can be encoded in F-PRISMA. Finally, we show that basic categorical tools can help to relate and to compose SAMs and PRISMA processes in an elegant way.     

On the Expressive Power of Polyadic Synchronisation in π-calculus

We extend the π-calculus with polyadic synchronisation, a generalisation of the communication mechanism which allows channel names to be composite. We show that this operator embeds nicely in the theory of π-calculus, and makes it possible to derive divergence-free encodings of distributed calculi. We give a separation result between the π-calculus with polyadic synchronisation (^eπ) and the original calculus, in the style of an analogous result given by Palamidessi for mixed choice. We encode Local Area π showing how to control the local use of resources in ^eπ.     

Interaction Nets vs. the ρ-calculus: Introducing Bigraphical Nets

The ρ-calculus generalises both term rewriting and the λ-calculus in a uniform framework. Interaction nets are a form of graph rewriting which proved most successful in understanding the dynamics of the λ-calculus, the prime example being the implementation of optimal β-reduction. It is thus natural to study interaction net encodings of the ρ-calculus as a first step towards the definition of efficient reduction strategies. We give two interaction net encodings which bring a new understanding to the operational semantics of the ρ-calculus; however, these encodings have some drawbacks and to overcome them we introduce bigraphical nets—a new paradigm of computation inspired by Lafont's interactions nets and Milner's bigraphs.     

Interaction in Time and Space

Distributed π-calculus and ambient calculus are extended with timers which may trigger timeout recovery processes. Timers provide a useful notion of relative time with respect to the interaction in a distributed system. The rather flat notion of space in timed distributed π-calculus is improved by considering a hierarchical representation of space in timed mobile ambients. Some basic results are proven, making sound both formal approaches. An easily understood example is used for both extensions, showing how it is possible to describe a non-monotonic behaviour and use a decentralized control to coordinate the interacting components in time and space.     

Probabilistic π-Calculus and Event Structures

This paper proposes two semantics of a probabilistic variant of the π-calculus: an interleaving semantics in terms of Segala automata and a true concurrent semantics, in terms of probabilistic event structures. The key technical point is a use of types to identify a good class of non-deterministic probabilistic behaviours which can preserve a compositionality of the parallel operator in the event structures and the calculus. We show an operational correspondence between the two semantics. This allows us to prove a “probabilistic confluence” result, which generalises the confluence of the linearly typed π-calculus.     

On the representation of McCarthy's in the -calculus

We study the encoding of , the call-by-name λ-calculus enriched with McCarthy's amb operator, into the π-calculus. Semantically, amb is a challenging operator, for the fairness constraints that it expresses. We prove that, under a certain interpretation of divergence in the λ-calculus (weak divergence), a faithful encoding is impossible. However, with a different interpretation of divergence (strong divergence), the encoding is possible, and for this case we derive results and coinductive proof methods to reason about that are similar to those for the encoding of pure λ-calculi. We then use these methods to derive the most important laws concerning amb. We take bisimilarity as behavioural equivalence on the π-calculus, which sheds some light on the relationship between fairness and bisimilarity.     

Separation of Synchronous and Asynchronous Communication Via Testing

One of the early results about the asynchronous π-calculus which significantly contributed to its popularity is the capability of encoding the output prefix of the (choiceless) π-calculus in a natural and elegant way. Encodings of this kind were proposed by Honda and Tokoro, by Nestmann and (independently) by Boudol. We investigate whether the above encodings preserve De Nicola and Hennessy's testing semantics. In this sense, it turns out that, under some general conditions, no encoding of output prefix is able to preserve the must testing. This negative result is due to (a) the non atomicity of the sequences of steps which are necessary in the asynchronous π-calculus to mimic synchronous communication, and (b) testing semantics's sensitivity to divergence.     

From Functional Programs to Interaction Nets via the Rewriting Calculus

We use the ρ-calculus as an intermediate language to compile functional languages with pattern-matching features, and give an interaction net encoding of the ρ-terms arising from the compilation. This encoding gives rise to new strategies of evaluation, where pattern-matching and 'traditional' β-reduction can proceed in parallel without overheads.     

Linearity, Persistence and Testing Semantics in the Asynchronous Pi-Calculus

In [C. Palamidessi, V. Saraswat, F. Valencia and B. Victor. On the Expressiveness of Linearity vs Persistence in the Asynchronous Pi Calculus. LICS 2006:59–68, 2006] the authors studied the expressiveness of persistence in the asynchronous π-calculus (Aπ) wrt weak barbed congruence. The study is incomplete because it ignores the issue of divergence. In this paper, we present an expressiveness study of persistence in the asynchronous π-calculus (Aπ) wrt De Nicola and Hennessy's testing scenario which is sensitive to divergence. Following [C. Palamidessi, V. Saraswat, F. Valencia and B. Victor. On the Expressiveness of Linearity vs Persistence in the Asynchronous Pi Calculus. LICS 2006:59–68, 2006], we consider Aπ and three sub-languages of it, each capturing one source of persistence: the persistent-input calculus (PIAπ), the persistent-output calculus (POAπ) and persistent calculus (PAπ). In [C. Palamidessi, V. Saraswat, F. Valencia and B. Victor. On the Expressiveness of Linearity vs Persistence in the Asynchronous Pi Calculus. LICS 2006:59–68, 2006] the authors showed encodings from Aπ into the semi-persistent calculi (i.e., POAπ and PIAπ) correct wrt weak barbed congruence. In this paper we prove that, under some general conditions, there cannot be an encoding from Aπ into a (semi)-persistent calculus preserving the must testing semantics.     

On the decidability of fragments of the asynchronous π-calculus

We study the decidability of a reachability problem for various fragments of the asynchronous π-calculus. We consider the combination of three main features: name generation, name mobility, and unbounded control. We show that the combination of name generation with either name mobility or unbounded control leads to an undecidable fragment. On the other hand, we prove that name generation without name mobility and with bounded control is decidable by reduction to the coverability problem for Petri Nets.     

On the Expressive Power of Klaim-based Calculi

In this work, we study the expressive power of variants of Klaim, an experimental language with programming primitives for global computing that combines the process algebra approach with the coordination-oriented one. Klaim has proved to be suitable for programming a wide range of distributed applications with agents and code mobility, and has been implemented on the top of a runtime system based on Java. The expressivity of its constructs is tested by distilling from it some (more and more foundational) calculi and studying the encoding of each of the considered languages into a simpler one. An encoding of the asynchronous π-calculus into one of these calculi is also presented.     

A CPS Encoding of Name-Passing in Higher-Order Mobile Embedded Resources

We present an encoding of the synchronous π-calculus in the calculus of Higher-Order Mobile Embedded Resources (Homer), a pure higher-order calculus with mobile processes in nested locations, defined as a simple, conservative extension of the core process-passing subset of Thomsen's Plain CHOCS. We prove that our encoding is fully abstract with respect to barbed bisimulation and sound with respect to barbed congruence. Our encoding demonstrates that higher-order process-passing together with mobile resources in (local) named locations are sufficient to express π-calculus name-passing. The encoding uses a novel continuation passing style to facilitate the encoding of synchronous communication.     

On the Expressiveness of Chi, Update, and Fusion calculi

Chi and Update calculi [9,17] have been independently introduced in order to model mobile systems. The two calculi are very close to each other and represent an evolution of π-calculus [15]. More recently a (non-straightforward) polyadic version of the Update calculus, the Fusion calculus, has been proposed [18].In the paper we give a fully abstract encoding from an asynchronous variant of Chi and Update calculi to asynchronous π-calculus [11,4]. This proves that, at least for their asynchronous variants, Chi and Update calculi are not more expressive than π-calculus. A similar result can be proved for the Fusion calculus.     

A Proof Search Specification of the π-Calculus

We present a meta-logic that contains a new quantifier (for encoding “generic judgments”) and inference rules for reasoning within fixed points of a given specification. We then specify the operational semantics and bisimulation relations for the finite π-calculus within this meta-logic. Since we restrict to the finite case, the ability of the meta-logic to reason within fixed points becomes a powerful and complete tool since simple proof search can compute this one fixed point. The quantifier helps with the delicate issues surrounding the scope of variables within π-calculus expressions and their executions (proofs). We shall illustrate several merits of the logical specifications we write: they are natural and declarative; they contain no side conditions concerning names of variables while maintaining a completely formal treatment of such variables; differences between late and open bisimulation relations are easy to see declaratively; and proof search involving the application of inference rules, unification, and backtracking can provide complete proof systems for both one-step transitions and for bisimulation.     

Timers for Distributed Systems

We deal with temporal aspects of distributed systems, introducing and studying a new model called timed distributed π-calculus. This model extends distributed π-calculus with timers, transforming the communication channels into temporary resources. Distributed π-calculus describes located interactions between processes with restricted access to resources. We introduce time constraints by considering timeout timers for channels. Combining these timers with types and locations, we provide a formal framework able to describe complex systems with constraints on time and on resource access. Its typing system and operational semantics are presented. It is proved that the passage of time does not interfere with the typing system. The new model is proved to be sound by using a method based on subject reduction.