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.     

Structured coalgebras and minimal HD-automata for the -calculus

The coalgebraic framework developed for the classical process algebras, and in particular its advantages concerning minimal realizations, does not fully apply to the π-calculus, due to the constraints on the freshly generated names that appear in the bisimulation.In this paper we propose to model the transition system of the π-calculus as a coalgebra on a category of name permutation algebras and to define its abstract semantics as the final coalgebra of such a category. We show that permutations are sufficient to represent in an explicit way fresh name generation, thus allowing for the definition of minimal realizations.We also link the coalgebraic semantics with a slightly improved version of history dependent (HD) automata, a model developed for verification purposes, where states have local names and transitions are decorated with names and name relations. HD-automata associated with agents with a bounded number of threads in their derivatives are finite and can be actually minimized. We show that the bisimulation relation in the coalgebraic context corresponds to the minimal HD-automaton.     

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 allπ-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. Received: June 11, 1993/November 28, 1994     

Presheaf models for CCS-like languages

The aim of this paper is to harness the mathematical machinery around presheaves for the purposes of process calculi. Joyal, Nielsen and Winskel proposed a general definition of bisimulation from open maps. Here we show that open-map bisimulations within a range of presheaf models are congruences for a general process language, in which CCS and related languages are easily encoded. The results are then transferred to traditional models for processes. By first establishing the congruence results for presheaf models, abstract, general proofs of congruence properties can be provided and the awkwardness caused through traditional models not always possessing the cartesian liftings, used in the breakdown of process operations, are side stepped. The abstract results are applied to show that hereditary history-preserving bisimulation is a congruence for CCS-like languages to which is added a refinement operator on event structures as proposed by van Glabbeek and Goltz.     

Computing Bisimulations for Finite-Controlπ-Calculus

Symbolic bisimulation avoids the infinite branching problem caused by instantiating input names with all names in the standard definition of bisimulation in π-calculus.However,it does not automatically lead to an efficient algorithm,because symbolic bisimulation is indexed by conditions on names,and directly manipulating such conditions can be computationally costly.In this paper a new notion of bisimulation is introduced,in which the manipulation of maximally consistent conditions is replaced with a systematic employment of schematic names.It is shown that the new notion captures symbolic bisimulation in a precise sense.Based on the new definition an efficient algorithm,which instantiates input names “on-the -fly“,is presented to check bisimulations for finite-control π-calculus.     

传值系统的互模拟与谓词等式系

本文引入描述传值并系统的新模型“带赋值符号迁移图（ＳＴＧＡ）”推广了Ｈｅｎｎｅｓｓｙ和Ｌｉｎ提出的“符号迁移图”的概念，允许迁移上带有赋值，从而能将更大的一类传值系统表示为有穷状态图，ＳＴＧＡ的中车优点是在并行运算不封闭，文中给给ＳＴＧＡ的操作语义，在此基础上定义了ＳＴＧＡ的互模拟等价关系，为了刻划ＳＴＧＡ的互模拟，以谓词等式系的形式在一阶逻辑的正子集中扩充了最大和最小不动点，并设计了一个算法将Ｓ     

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.     

O-Minimal Hybrid Systems

An important approach to decidability questions for verification algorithms of hybrid systems has been the construction of a bisimulation. Bisimulations are finite state quotients whose reachability properties are equivalent to those of the original infinite state hybrid system. In this paper we introduce the notion of o-minimal hybrid systems, which are initialized hybrid systems whose relevant sets and flows are definable in an o-minimal theory. We prove that o-minimal hybrid systems always admit finite bisimulations. We then present specific examples of hybrid systems with complex continuous dynamics for which finite bisimulations exist. Date received: June 9, 1998. Date revised: June 28, 1999.     

Partition refinement of Component Interaction Automata

Component Interaction Automata provide a fitting model to capture and analyze the temporal facets of hierarchically-structured component-oriented software systems. However, the rules governing composition typically suffer from combinatorial state explosion, an effect that can impede modeling languages, like Component Interaction Automata, from being successful in real-world scenarios. We must, therefore, find some appropriate ways to counteract state explosion, one of which is partition refinement through bisimulation, in particular, weak bisimulation. While this technique can yield the desired state space reduction, it does not consider synchronization cliques, that is, groups of states that are interconnected solely by internal synchronization transitions. Synchronization cliques give rise to action prefixes, local states that encapsulate pre-conditions for a component’s ability to interact with the environment. Furthermore, both the existence and the size of synchronization cliques can be used as an indicator for the success of partition refinement. In particular, the more frequent synchronization cliques are and the more states they entail, the more likely it is that partition refinement can reduce the state space. But, there may be other factors that impact the refinement process. For this reason, we study, in this paper, how partition refinement behaves under weak bisimulation, how synchronization cliques emerge when using weak bisimulation, how we make state space reduction through partition refinement aware of the existence of synchronization cliques, and what other attributes of Component Interaction Automata specifications can provides us with additional cues to forecast the possible outcome of the partition refinement process.     

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.     

A Coinduction Principle for Recursive Data Types Based on Bisimulation

The concept of bisimulation from concurrency theory is used to reason about recursively defined data types. From two strong-extensionality theorems stating that the equality (resp. inequality) relation is maximal among all bisimulations, a proof principle for the final coalgebra of an endofunctor on a category of data types (resp. domains) is obtained. As an application of the theory developed, an internal full abstraction result (in the sense of S. Abramsky and C.-H. L. Ong [Inform. and Comput.105, 159–267 (1993)] for the canonical model of the untyped call-by-valueλ-calculus is proved. Also, the operational notion of bisimulation and the denotational notion of final semantics are related by means of conditions under which both coincide.     

Models for name-passing processes: interleaving and causal

We study syntax-free models for name-passing processes. For interleaving semantics, we identify the indexing structure required of an early labelled transition system to support the usual π-calculus operations, defining Indexed Labelled Transition Systems. For non-interleaving causal semantics we define Indexed Labelled Asynchronous Transition Systems, smoothly generalizing both our interleaving model and the standard Asynchronous Transition Systems model for CCS-like calculi. In each case we relate a denotational semantics to an operational view, for bisimulation and causal bisimulation respectively. We establish completeness properties of, and adjunctions between, categories of the two models. Alternative indexing structures and possible applications are also discussed. These are first steps towards a uniform understanding of the semantics and operations of name-passing calculi.     

Congruence of Bisimulation in a Non-Deterministic Call-By-Need Lambda Calculus

We present a call-by-need λ-calculus λ_ND with an erratic non-deterministic operator pick and a non-recursive let. A definition of a bisimulation is given, which has to be based on a further calculus named λ_≈, since the naïve bisimulation definition is useless. The main result is that bisimulation in λ_≈ is a congruence and coincides with the contextual equivalence. The proof is a non-trivial extension of Howe's method. This might be a step towards defining useful bisimulation relations and proving them to be congruences in calculi that extend the λ_ND-calculus.     

Exploring probabilistic bisimulations, part I

We take a fresh look at strong probabilistic bisimulations for processes which exhibit both non-deterministic and probabilistic behaviour. We suggest that it is natural to interpret such processes as distributions over states in a probabilistic labelled transition system, a pLTS; this enables us to adapt the standard notion of contextual equivalence to this setting. We then prove that a novel form of bisimulation equivalence between distributions are both sound and complete with respect to this contextual equivalence. We also show that a very simple extension to HML, Hennessy–Milner Logic, provides finite explanations for inequivalences between distributions. Finally we show that our bisimulations between distributions in a pLTS are simply an alternative characterisation of a standard notion of probabilistic bisimulation equivalence, defined between states in a pLTS.     

A theory of processes with localities

We study a notion of observation for concurrent processes which allows the observer to see the distributed nature of processes, giving explicit names for the location of actions. A general notion of bisimulation related to this observation of distributed systems is introduced. Our main result is that these bisimulation relations, particularized to a process algebra extending CCS, are completely axiomatizable. We discuss in detail two instances of location bisimulations, namely the location equivalence and the location preorder.This work has been partly supported by the ESPRIT/BRA project CEDISYS.     

Comparing locality and causality based equivalences

For CCS [15] several noninterleaving semantics have been proposed among which causal bisimulation [9] and location equivalence [6] play a central role. To unify these two approaches this paper introduces a new transition system based onlocal andglobal causes. Bisimulation equivalence is parameterized by a functionf which evaluates the information on causes provided by the transitions. Appropriate instantiations off yield characterizations of causal bisimulations and location equivalence.     

Local abstraction–refinement for the <Emphasis Type="Italic">μ</Emphasis>-calculus

A key technique for the verification of programs is counterexample-guided abstraction–refinement (CEGAR). Grumberg et al. (LNCS, vol 3385, pp. 233–249. Springer, Berlin, 2005; Inf Comput 205(8):1130–1148, 2007) developed a CEGAR-based algorithm for the modal μ-calculus. There, every abstract state is split in a refinement step. In this paper, the work of Grumberg et al. is generalized by presenting a new CEGAR-based algorithm for the μ-calculus. It is based on a more expressive abstract model and applies refinement only locally (at a single abstract state), i.e., the lazy abstraction technique for safety properties is adapted to the μ-calculus. Furthermore, it separates refinement determination from the (3-valued based) model checking. Three different heuristics for refinement determination are presented and illustrated.     

Bisimulation for Higher-Order Process Calculi

Ahigher-order process calculusis a calculus for communicating systems which contains higher-order constructs like communication of terms. We analyse the notion ofbisimulationin these calculi. We argue that both the standard definition of bisimulation (i.e., the one for CCS and related calculi), as well ashigher-order bisimulation[E. Astesiano, A. Giovini, and G. Reggio,in“STACS '88,” Lecture Notes in Computer Science, Vol. 294, pp. 207–226, Springer-Verlag, Berlin/New York, 1988; G. Boudol,in“TAPSOFT '89,” Lecture Notes in Computer Science, Vol. 351, pp. 149–161, Springer-Verlag, Berlin/New York, 1989; B. Thomsen, Ph.D. thesis, Dept. of Computing, Imperial College, 1990] are in general unsatisfactory, because of their over-discrimination. We propose and study a new form of bisimulation for such calculi, calledcontext bisimulation, which yields a more satisfactory discriminanting power. A drawback of context bisimulation is the heavy use of universal quantification in its definition, which is hard to handle in practice. To resolve this difficulty we introducetriggered bisimulationandnormal bisimulation, and we prove that they both coincide with context bisimulation. In the proof, we exploit thefactorisation theorem: When comparing the behaviour of two processes, it allows us to “isolate” subcomponents which might give differences, so that the analysis can be concentrated on them     

Bisimulation for Labelled Markov Processes

In this paper we introduce a new class of labelled transition systems—labelled Markov processes— and define bisimulation for them. Labelled Markov processes are probabilistic labelled transition systems where the state space is not necessarily discrete. We assume that the state space is a certain type of common metric space called an analytic space. We show that our definition of probabilistic bisimulation generalizes the Larsen–Skou definition given for discrete systems. The formalism and mathematics is substantially different from the usual treatment of probabilistic process algebra. The main technical contribution of the paper is a logical characterization of probabilistic bisimulation. This study revealed some unexpected results, even for discrete probabilistic systems.

• Bisimulation can be characterized by a very weak modal logic. The most striking feature is that one has no negation or any kind of negative proposition.

• We do not need any finite branching assumption, yet there is no need of infinitary conjunction.

We also show how to construct the maximal autobisimulation on a system. In the finite state case, this is just a state minimization construction. The proofs that we give are of an entirely different character than the typical proofs of these results. They use quite subtle facts about analytic spaces and appear, at first sight, to be entirely nonconstructive. Yet one can give an algorithm for deciding bisimilarity of finite state systems which constructs a formula that witnesses the failure of bisimulation.