Barbed Equivalence Research Articles

Concurrency cannot be observed, asynchronously

The paper is devoted to an analysis of the concurrent features of asynchronous systems. A preliminary step is represented by the introduction of a non-interleaving extension of barbed equivalence. This notion is then exploited in order to prove thatconcurrency cannot be observedthrough asynchronous interactions, i.e., that the interleaving and concurrent versions of a suitable asynchronous weak equivalence actually coincide. The theory is validated on some case studies, related to nominal calculi (π-calculus) and visual specification formalisms (Petri nets). Additionally, we prove that a class of systems which is deemed (output-buffered) asynchronous, according to a characterization that was previously proposed in the literature, falls into our theory.

Behavioural equivalences of a probabilistic pi-calculus

Although different kinds of probabilistic π-calculus have been introduced and found their place in quantitative verification and evaluation, their behavioural equivalences still lack a deep investigation. We propose a simple probabilistic extension of the π-calculus, πp, which is inspired by Herescu and Palamidessi’s probabilistic asynchronous π-calculus. An early semantics of our πp is presented. We generalise several classic behavioural equivalences to probabilistic versions, obtaining the probabilistic (strong) barbed equivalence and probabilistic bisimulation for πp. Then we prove that the coincidence between the barbed equivalence and bisimilarity in the π-calculus is preserved in the probabilistic setting.

Value-passing CCS with noisy channels

Value-passing CCS, a full version of Milner’s CCS, is a process algebra in which actions consist of sending and receiving values through noiseless communication channels. The full calculus is a succinct yet expressive language for the specification and verification of reactive systems. Taking into account the reality of channel noise in reactive systems, in this paper we introduce an extension of value-passing CCS, called value-passing CCS with noisy channels (VCCSN), in which noise is described by a probability distribution over the values. After presenting the reduction operational semantics and labelled operational semantics of VCCSN, we develop the theory of behavioural equivalence by introducing barbed equivalence, barbed congruence, bisimilarity, and full bisimilarity. In particular, we show that barbed equivalence and barbed congruence coincide with bisimilarity and full bisimilarity, respectively. Based upon the labelled operational semantics of VCCSN, we establish a probabilistic modal logic for expressing system properties and show its connection with the notion of bisimilarity. Finally, we use VCCSN to model a communication protocol for ensuring the reliable transmission of data across an error-prone channel.

A Hierarchy of Behavioral Equivalences in the -calculus with Noisy Channels

The π-calculus is a process algebra where agents interact by sending communication links to each other via noiseless communication channels. Taking into account the reality of noisy channels, an extension of the π-calculus, called the πN-calculus, has been introduced recently. This paper presents an early transitional semantics of the πN-calculus, which is not a directly translated version of the late semantics of πN, and then extends six kinds of behavioral equivalences consisting of reduction bisimilarity, barbed bisimilarity, barbed equivalence, barbed congruence, bisimilarity and full bisimilarity into the πN-calculus. Such behavioral equivalences are cast in a hierarchy, which is helpful to verify behavioral equivalence of two agents. In particular, this paper shows that due to the noisy nature of channels, the coincidence of bisimilarity and barbed equivalence, as well as the coincidence of full bisimilarity and barbed congruence, in the π-calculus does not hold in πN.

XPi: A typed process calculus for XML messaging

We present XPi , a core calculus for XML messaging. XPi features asynchronous communication, pattern matching, name and code mobility, integration of static and dynamic typing. In XPi , a type system disciplines XML message handling at the level of channels, patterns, and processes. A run-time safety theorem ensures that in well-typed systems no service will ever receive documents it cannot understand, and that the offered services will be consistent with the declared channel capacities. An inference system is introduced, which is proved to be in full agreement with type checking. A notion of barbed equivalence is defined that takes into account information about service interfaces. Flexibility and expressiveness of this calculus are illustrated by a number of examples, some concerning description and discovery of web services.

Contextual Labelled Semantics for Higher-order Process Calculi

In this paper, we study a contextual labelled transition semantics for Higher-Order process calculi. The labelled transition semantics are relatively clean and simple, and corresponding bisimulation equivalence can be easily formulated based on it. Besides we develop a novel approach to reason about behaviours of a higher-order substituted process P{Q/X}, based on which we can directly prove a very important result – factorisation theorem. To show the correspondence between our semantics and the well-established ones, we characterize our bisimulation in a version of barbed equivalence.

Towards a theory of bisimulation for the higher-order process calculi

In this paper, a labelled transition semantics for higher-order process calculi is studied. The labelled transition semantics is relatively clean and simple, and corresponding bisimulation equivalence can be easily formulated based on it. And the congruence properties of the bisimulation equivalence can be proved easily. To show the correspondence between the proposed semantics and the well-established ones, the bisimulation is characterized as a version of barbed equivalence and a version of context bisimulation.

Proof Techniques for Cryptographic Processes

Contextual equivalences for cryptographic process calculi, like the spi-calculus, can be used to reason about correctness of protocols, but their definition suffers from quantification over all possible contexts. Here, we focus on two such equivalences, namely may-testing and barbed equivalence, and investigate tractable proof methods for them. To this aim, we design an enriched labelled transition system, where transitions are constrained by the knowledge the environment has of names and keys. The new transition system is then used to define a trace equivalence and a weak bisimulation equivalence that avoid quantification over contexts. Our main results are soundness and completeness of trace and weak bisimulation equivalence with respect to may-testing and barbed equivalence, respectively. They lead to more direct proof methods for equivalence checking. The use of these methods is illustrated with a few examples concerning implementation of secure channels and verification of protocol correctness.

On bisimulations for the asynchronous π-calculus

The asynchronous π-calculus is a variant of the π-calculus where message emission is non-blocking. Honda and Tokoro have studied a semantics for this calculus based on bisimulation. Their bisimulation relies on a modified transition system where, at any moment, a process can perform any input action. In this paper we propose a new notion of bisimulation for the asynchronous π-calculus, defined on top of the standard labelled transition system. We give several characterizations of this equivalence including one in terms of Honda and Tokoro's bisimulation, and one in terms of barbed equivalence. We show that this bisimulation is preserved by name substitutions, hence by input prefix. Finally, we give a complete axiomatization of the (strong) bisimulation for finite terms.