Open Bisimulation Research Articles

Verification of critical systems described in real-time TiMo

We present a simple prototyping language for describing real-time systems including specific features as timeouts, explicit locations, timed migration and timed communication. The parallel execution of a step is provided by multiset labelled transitions. To illustrate its features, we describe a railway control system, and define some behavioural equivalences matching multisets of actions that could happen in a given interval of time. We define strong time-bounded bisimulation and strong open time-bounded bisimulation, and prove that the latter one is a congruence. By using various bisimulations over the behaviours of real-time systems, we can check which behaviours are closer to an optimal and safe behaviour. Automatic analysis is performed using a verification platform called TiMo@PAT which supports the verification of domain-specific properties like process location reachability, time-bounded properties, as well as optimizing resources.

Symbolic Bisimulation for Quantum Processes

With the previous notions of bisimulation presented in the literature, to check if two quantum processes are bisimilar, we have to instantiate their free quantum variables with arbitrary quantum states, and verify the bisimilarity of the resulting configurations. This makes checking bisimilarity infeasible from an algorithmic point of view, because quantum states constitute a continuum. In this article, we introduce a symbolic operational semantics for quantum processes directly at the quantum operation level, which allows us to describe the bisimulation between quantum processes without resorting to quantum states. We show that the symbolic bisimulation defined here is equivalent to the open bisimulation for quantum processes in previous work, when strong bisimulations are considered. An algorithm for checking symbolic ground bisimilarity is presented. We also give a modal characterisation for quantum bisimilarity based on an extension of Hennessy-Milner logic to quantum processes.

Proof search specifications of bisimulation and modal logics for the π-calculus

We specify the operational semantics and bisimulation relations for the finite φ-calculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allows this logic to be complete for both the inductive nature of operational semantics and the coinductive nature of bisimulation. The ∇ quantifier helps with the delicate issues surrounding the scope of variables within φ-calculus expressions and their executions (proofs). We illustrate several merits of the logical specifications permitted by this logic: 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 arise from familar logic distinctions; the interplay between the three quantifiers (∀, ∃, and ∇) and their scopes can explain the differences between early and late bisimulation and between various modal operators based on bound input and output actions; and proof search involving the application of inference rules, unification, and backtracking can provide complete proof systems for one-step transitions, bisimulation, and satisfaction in modal logic. We also illustrate how one can encode the φ-calculus with replications, in an extended logic with induction and co-induction.

An Open Approach for the Applied Pi Calculus

A notion of open bisimulation is proposed for the Applied Pi Calculus, which extends π-calculus in order to facilitate analyzing security protocols. Our notion is based on the labeled transition system, and takes a knowledge aware open approach to model knowledge in security protocols. It is shown to be sound to labeled bisimilarity and is a congruent relation. As a running example, we analyze two e-commerce protocol, namely iKP and Ferguson’s electronic cash protocol, by Applied Pi and open bisimilarity.

Open bisimulation, revisited

In the context of the π -calculus, open bisimulation is prominent and popular due to its congruence properties and its easy implementability. Motivated by the attempt to generalise it to the spi-calculus, we offer a new, more refined definition and show how far it coincides with the original one.

Open Bisimulation, Revisited

In the context of the π-calculus, open bisimulation is prominent and popular due to its congruence properties and its easy implementability. Motivated by the attempt to generalise it to the spi-calculus, we offer a new, more refined definition and show in how far it coincides with the original one.

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.

Relationally Staged Computations in Calculi of Mobile Processes

We apply the recently developed techniques of higher order abstract syntax and functorial operational semantics to give a compositional and fully abstract semantics for the π-calculus equipped with open bisimulation. The key novelty in our work is the realisation that the sophistication of open bisimulation requires us to move from the usual semantic domain of presheaves over subcategories of Set to presheaves over subcategories of Rel. This extra structure is crucial in controlling the renaming of extruded names and in providing a variety of different dynamic allocation operators to model the different binders of the π-calculus.

Checking for Open Bisimilarity in the pi-Calculus

<p>This paper deals with algorithmic checking of open bisimilarity in the pi-calculus. Most bisimulation checking algorithms are based on the partition refinement approach. Unfortunately the definition of open bisimulation does not permit us to use a partition refinement approach for open bisimulation checking directly, but in the paper 'A Partition Refinement Algorithm for the pi-Calculus' Marco Pistore and Davide Sangiorgi present an iterative method that makes it possible to check for open bisimilarity using partition refinement. We have implemented the algorithm presented by Marco Pistore and Davide Sangiorgi. Furthermore,<br />we have optimized this algorithm and implemented this optimized algorithm. The time-complexity of this algorithm is the same as the time-complexity for the first algorithm, but performance tests have shown that in many cases the running time of the optimized algorithm is shorter than the running time of the first algorithm. Our implementation of the optimized open bisimulation checker algorithm and a user interface have been integrated in a system called the OBC Workbench.The source code and a manual for it is available from http://www.cs.auc.dk/research/FS/ny/PR-pi/.</p>

A Partition Refinement Algorithm for the π-Calculus

The partition refinement algorithm is the basis for most of the tools for checking bisimulation equivalences and for computing minimal realisations of CCS-like finite state processes. In this paper, we present a partition refinement algorithm for the π-calculus, a development of CCS where channel names can be communicated. It can be used to check bisimilarity and to compute minimal realisations of finite control processes—the π-calculus counterpart of CCS finite state processes. The algorithm is developed for strong open bisimulation and can be adapted to late and early bisimulations, as well as to weak bisimulations. To arrive at the algorithm, a few laws, proof techniques, and four characterizations of open bisimulation are proved.

A theory of bisimulation for the π-calculus

We study a new formulation of bisimulation for the π-calculus [MPW92], which we have called open bisimulation ( ∼ ). In contrast with the previously known bisimilarity equivalences, ∼ is preserved by all π-calculus operators, including input prefix. The differences among all these equivalences already appear in the sublanguage without name restrictions: Here the definition of ∼ can be factorised into a “standard” part which, modulo the different syntax of actions, is the CCS bisimulation, and a part specific to the π-calculus, which requires name instantiation. Attractive features of ∼ are: A simple axiomatisation (of the finite terms), with a completeness proof which leads to the construction of minimal canonical representatives for the equivalence classes of ∼; an “efficient” characterisation, based on a modified transition system. This characterisation seems promising for the development of automated-verification tools and also shows the call-by-need flavour of ∼. Although in the paper we stick to the π-calculus, the issues developed may be relevant to value-passing calculi in general.

Bisimulations for Asynchronous Mobile Processes

Within the past few years there has been renewed interest in the<br />study of value-passing process calculi as a consequence of the emergence of the pi-calculus. Here, [MPW89] have determined two variants of the notion of bisimulation, late and early bisimilarity. Most recently [San93] has proposed the new notion of open bisimulation equivalence. <br />In this paper we consider Plain LAL, a mobile process calculus which differs from the pi-calculus in the sense that the communication of data values happens asynchronously. The surprising result is that in the presence of asynchrony, the open, late and early bisimulation equivalences coincide - this in contrast to the pi-calculus where they are distinct. The result allows us to formulate a common equational theory which is sound and complete for finite terms of Plain LAL.