CCS-like Languages Research Articles

Equations, Contractions, and Unique Solutions

One of the most studied behavioural equivalences is bisimilarity. Its success is much due to the associated bisimulation proof method, which can be further enhanced by means of “bisimulation up-to” techniques such as “up-to context.” A different proof method is discussed, based on a unique solution of special forms of inequations called contractions and inspired by Milner’s theorem on unique solution of equations. The method is as powerful as the bisimulation proof method and its “up-to context” enhancements. The definition of contraction can be transferred onto other behavioural equivalences, possibly contextual and non-coinductive. This enables a coinductive reasoning style on such equivalences, either by applying the method based on unique solution of contractions or by injecting appropriate contraction preorders into the bisimulation game. The techniques are illustrated in CCS-like languages; an example dealing with higher-order languages is also shown.

Equations, Contractions, and Unique Solutions

One of the most studied behavioural equivalences is bisimilarity. Its success is much due to the associated bisimulation proof method, which can be further enhanced by means of "up-to bisimulation" techniques such as "up-to context". A different proof method is discussed, based on unique solution of special forms of inequations called contractions, and inspired by Milner's theorem on unique solution of equations. The method is as powerful as the bisimulation proof method and its "up-to context" enhancements. The definition of contraction can be transferred onto other behavioural equivalences, possibly contextual and noncoinductive. This enables a coinductive reasoning style on such equivalences, either by applying the method based on unique solution of contractions, or by injecting appropriate contraction preorders into the bisimulation game. The techniques are illustrated on CCS-like languages; an example dealing with higher-order languages is also shown.

Explicit fairness in testing semantics

In this paper we investigate fair computations in the pi-calculus. Following Costa and Stirling's approach for CCS-like languages, we consider a method to label process actions in order to filter out unfair computations. We contrast the existing fair-testing notion with those that naturally arise by imposing weak and strong fairness. This comparison provides insight about the expressiveness of the various `fair' testing semantics and about their discriminating power.

The Saga of the Axiomatization of Parallel Composition

This paper surveys some classic and recent results on the finite axiomatizability of bisimilarity over CCS-like languages. It focuses, in particular, on non-finite axiomatizability results stemming from the semantic interplay between parallel composition and nondeterministic choice. The paper also highlights the role that auxiliary operators, such as Bergstra and Klop's left and communication merge and Hennessy's merge operator, play in the search for a finite, equational axiomatization of parallel composition both for classic process algebras and for their real-time extensions.

Fair Π

In this paper, we define fair computations in the π-calculus [Milner, R., Parrow, J. & Walker, D., A Calculus of Mobile Processes, Part I and II, Information and Computation 100 (1992) 1–78]. We follow Costa and Stirling's approach for CCS-like languages [Costa, G. & Stirling, C., A Fair Calculus of Communicating Systems, Acta Informatica 21 (1984) 417–441, Costa, G. & Stirling, C., Weak and Strong Fairness in CCS, Information and Computation 73 (1987) 207–244] but exploit a more natural labeling method of process actions to filter out unfair process executions. The new labeling allows us to prove all the significant properties of the original one, such as unicity, persistence and disappearance of labels. It also turns out that the labeled π-calculus is a conservative extension of the standard one. We contrast the existing fair testing [Brinksma, E., Rensink, A. & Vogler, W., Fair Testing, Proc. of CONCUR'95, LNCS, 962 (1995) 313–327, Natarajan, V. & Cleaveland, R., Divergence and Fair Testing, Proc. of ICALP '95, LNCS, 944 (1995) 648–659] with those that naturally arise by imposing weak and strong fairness as defined by Costa and Stirling. This comparison provides the expressiveness of the various fair testing-based semantics and emphasizes the discriminating power of the one already proposed in the literature.

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.

Presheaf Models for CCS-like Languages

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

Strong Fairness and Recursive Communicating Processes

Fairness — the guarantee that every process enabled sufficiently often will eventually make progress — provides a convenient and often useful abstraction from timing details that affect how parallel processes interact with one another. For processes that communicate via synchronous message passing, strong fairness is generally accepted as the most reasonable notion of fairness.This paper describes a strongly fair, trace-based semantics for a CCS-like language of communicating processes with full recursion. The semantics is a generalization of previous semantics for fair, imperative communicating processes. Unlike those earlier semantics, however, this semantics is not fully abstract: the combination of synchronous communication, fairness, and full recursion is extremely problematic. We outline the general difficulties encountered and discuss why the fair-trace approach is unlikely to yield full abstraction for this combination of features.

A fully abstract semantics for causality in the $\pi$ -calculus

We examine the meaning of causality in calculi for mobile processes like the $\pi$ -calculus, and we investigate the relationship between interleaving and causal semantics for such calculi. We separate two forms of causal dependencies on actions of $\pi$ -calculus processes, called subject and object dependencies: The former originate from the nesting of prefixes and are propagated through interactions among processes (they are the only form of causal dependencies present in CCS-like languages); the latter originate from the binding mechanisms on names. We propose a notion of causal bisimulation which distinguishes processes which differ for the subject or for the object dependencies. We show that this causal equivalence can be reconducted to, or implemented into, the ordinary interleaving observation equivalence. We prove that our encoding is fully abstract w.r.t. the two behavioural equivalences. This allows us to exploit the simpler theory of the interleaving semantics to reason about the causal one. In [San94b] a similar programme is carried out for location bisimulation [BCHK91], a non-interleaving spatial-sensitive (as opposed to causal-sensitive) behavioural equivalence. The comparison between the encodings of causal bisimulation in this paper, and of location bisimulation in [San94b], evidences the similarities and the differences between these two equivalences.

On the coarsest congruence within global-clock-bounded equivalence

Global-clock-bounded equivalence has been proposed in the literature as a performance-sensitive bisimulation-based semantics for CCS-like languages. It enjoys several pleasant properties but it is not a congruence with respect to parallel composition. In this paper we give a bisimulation-based characterization of the coarsest congruence contained within global-clock-bounded equivalence. The new equivalence is strictly related to another performance-sensitive equivalence proposed in the literature, lazy performance equivalence, and coincides with the latter when processes can perform visible actions only.

A Characterization of Finitary Bisimulation

Following a paradigm put forward by Milner and Plotkin, a primary criterion to judge the appropriateness of denotational models for programming and specification languages is that they be in agreement with operational intuition about program behaviour. Of the "good t" criteria for such models that have been<br />discussed in the literature, the most desirable one is that of full abstraction.<br />Intuitively, a fully abstract denotational model is guaranteed to relate exactly all those programs that are operationally indistinguishable with respect to some chosen notion of observation. <br />Because of its prominent role in process theory, bisimulation [12] has been a natural yardstick to assess the appropriateness of denotational models for several process description languages. In particular, when proving full abstraction<br />results for denotational semantics based on the Scott-Strachey approach for CCS-like languages, several preorders based on bisimulation have been considered; see, e.g., [6, 3, 4]. In this paper, we shall study one such bisimulationbased<br />preorder whose connections with domain-theoretic models are by now well understood, viz. the prebisimulation preorder . investigated in, e.g., [6, 3]. Intuitively, p < q holds of processes p and q if p and q can simulate each other's<br />behaviour, but at times the behaviour of p may be less specified than that of q. <br />A common problem in relating denotational semantics for process description<br />languages, based on Scott's theory of domains or on the theory of algebraic semantics, with behavioural semantics based on bisimulation is that the chosen behavioural theory is, in general, too concrete. The reason for this phenomenon is that two programs are related by a standard denotational interpretation if, in some precise sense, they afford the same finite observations. On the other hand, bisimulation can make distinctions between the behaviours of two processes<br />based on infinite observations. (Cf. the seminal study [1] for a detailed analysis of this phenomenon.) To overcome this mismatch between the denotational<br />and the behavioural theory, all the aforementioned full abstraction results are obtained with respect to the so-called finitely observable, or finitary, part of bisimulation. The finitary bisimulation is defined on any labelled transition system thus: p <^F q iff t < p implies t < q, for every finite synchronization tree t.<br /> An alternative characterization of the finitary bisimulation for arbitrary transition systems has been given by Abramsky in [1]. This characterization is couched in logical terms, and is an impressive byproduct of Abramsky's "theory<br />of domains in logical form" programme. More precisely, Abramsky shows that two processes in any transition system are equated by the finitary bisimulation<br />iff they satisfy the same formulae in the finitary version of the domain logic for transition systems. The existence of this logical view of the finitary bisimulation gives us a handle to work with this relation. However, an alternative,<br />behavioural view of the finitary bisimulation might be more useful when establishing results which are more readily shown on the behavioural, rather than on the logical, side. Examples of such results are complete axiomatizations for<br />the finitary bisimulation and full abstraction results. A behavioural characterization of the finitary bisimulation would also provide an easier way to establish when two processes in a transition system are related by it or not, thus giving more insight on the kind of identifications made by this relation. In this study, we offer a behavioural characterization of the finitary bisimulation<br />for arbitrary transition systems (cf. Thm. 3.5). This result may be seen as the behavioural counterpart of Abramsky's logical characterization theorem [1, Thm. 5.5.8]. Moreover, for the important class of sort-finite transition systems<br />we present a sharpened version of a behavioural characterization result first proven by Abramsky in [3, Propn. 6.13]. The interested reader may consult the unpublished report [5] for more results on the finitary bisimulation.

Failures, Finiteness and Full Abstraction

For a simple CCS-like language a trace semantics and a failure semantics are presented. The failure semantics is shown to be fully abstract with respect to the trace semantics if and only if the set of internal actions is infinite.

Two models of concurrent objects

Two models of concurrent objects