Split-2 Bisimilarity has a Finite Axiomatization over CCS with
Hennessy's Merge (original) (raw)
Related papers
Bisimulation equivalence is decidable for basic parallel processes
Lecture Notes in Computer Science, 1993
In a previous paper the authors proved the decidability of bisimulation equivalence over two subclasses of recurslve processes involving a parallel composition operator, namely the so-caUed norrned and live processes. In this paper, we extend this result to the whole class. The decidability proof permits us further to present a complete axiomatisation for this class of basic parallel processes. This result can be viewed as a proper extension of Miiner's complete axiomatisation of bisimulation equivalence on regular processes.
CCS with Hennessy's merge has no finite-equational axiomatization
Theoretical Computer Science, 2005
This paper confirms a conjecture of Bergstra and Klop's from 1984 by establishing that the process algebra obtained by adding an auxiliary operator proposed by Hennessy in 1981 to the recursion free fragment of Milner's Calculus of Communicating Systems is not finitely based modulo bisimulation equivalence. Thus, Hennessy's merge cannot replace the left merge and communication merge operators proposed by Bergstra and Klop, at least if a finite axiomatization of parallel composition modulo bisimulation equivalence is desired.
Finite equational bases in process algebra: Results and open questions
Processes, Terms and Cycles: Steps on the Road to Infinity, 2005
Van Glabbeek (1990) presented the linear time/branching time spectrum of behavioral equivalences for finitely branching, concrete, sequential processes. He studied these semantics in the setting of the basic process algebra BCCSP, and tried to give finite complete axiomatizations for them. Obtaining such axiomatizations in concurrency theory often turns out to be difficult, even in the setting of simple languages like BCCSP. This has raised a host of open questions that have been the subject of intensive research in recent years. Most of these questions have been settled over BCCSP, either positively by giving a finite complete axiomatization, or negatively by proving that such an axiomatization does not exist. Still some open questions remain. This paper reports on these results, and on the state-of-the-art in axiomatizations for richer process algebras with constructs like sequential and parallel composition.
Axiomatization of Bisimulation Based Relations
2005
The question of when two systems are behaviourally equal has occupied a large part of the literature on verification and has yielded various equivalences (and congruences). These equivalence relations are most useful in comparing systems whose executions are not necessarily finite. An axiomatization of these equivalences gives us both, a nice algebraic handle on processes, and a proof system for checking the equality of two processes. Comparison of efficiency of non-terminating processes like an operating system has been largely untackled. We have presented here, an axiomatization for a certain subset of ordering induced bisimilarities. This axiomatization yields the axiomatization for equivalences like observational equivalence and inefficiency bisimulation as special cases. The axiomatization has been proven to be complete for finite state processes, and can be used as a proof system for checking the equality of systems.
We study three notions of bisimulation equivalence for concurrent processes. Bisimulation equivalences are based on an operational interpretation of processes as labelled transition systems, and constitute the strongest notion of equivalence one may adopt for such systems: two systems are equivalent if and only if they have the same step-by-step behaviour. We focus first on Milner's notion of weak bisimulation (also known as observational equivalence) and propose an alternative formulation for it. More specifically, we show that Milner's notion may be redefined as one of reducibility to a same system-via a reduction function called abstraction homorriorphism. We use our characterisation to derive a complete set of reduction rules for observational equivalence on finite processes. We also show how abstraction homomorphisms may be extended to labelled event structures: however we do not consider the possibility of unobservable events here. We look then for notions of bisimulation which account for the concurrent aspects of processes. Traditional transition systems-evolving via successive elementary actions-only provide an interleaving semantics for concurrency. We suggest two generalisations of the notion of transition system: distributed transition systems, obtained by generalising the residual of a transition, and pornset transition systems, obtained by extending the notion of action labelling a transition (an action being now a partially ordered multiset). For the latter we find a corresponding notion of bisimulation on labelled event structures. Based on these new kinds of transitions, we obtain two bisimulation equivalences-one stronger than the other-which are both more discriminating than Milner's equivalence. For both of them we present an algebraic characterisation by means of a complete set of axioms.
1989
We study properties of equational characterisations of congruences defined over process algebras. The languages on which we concentrate are based on CCS, and our equivalences are generally restricted to observational congruences. We start by defining and investigating the notion of extensionality or w-completeness of an axiomatisation with respect to some semantic equivalence, as an extension of simple completeness, and show that, whereas in some cases the ability to wcompletely axiomatise a system is straightforward, there are sometimes difficulties in doing this when our algebra contains the symmetric full merge operator. We then consider the problem of decomposing a process into the parallel composition of simpler processes. Here we present several example systems where we can prove that any process term can be expressed uniquely as the parallel composition of prime process terms, those processes which cannot themselves be expressed as a parallel composition of at least two nontr...
Process Equivalences as Global Bisimulations
Zenodo (CERN European Organization for Nuclear Research), 2006
Bisimulation can be defined in a simple way using coinductive methods, and has rather pleasant properties. Ready similarity was proposed by Meyer et al. as a way to weakening the bisimulation equivalence thus getting a semantics defined in a similar way, but supported for more reasonable (weaker) observational properties. Global bisimulations were introduced by Frutos et al. in order to study different variants of non-determinism getting, in particular, a semantics under which the internal choice operator becomes associative. Global bisimulations are defined as plain bisimulations but allowing the use of new moves, called global transitions, that can change the processes not only locally in its head, but anywhere. Now we are continuing the study of global bisimulation but focusing on the way different semantics can be characterised as global bisimulation semantics. In particular, we have studied ready similarity, on the one hand because it was proposed as the strongest reasonable semantics weaker than bisimulation; on the other hand, because ready similarity was not directly defined as an equivalence relation but as the nucleus of an order relation, and this open the question whether it is also possible to define it as a symmetric bisimulation-like semantics. We have got a simple and elegant characterisation of ready similarity as a global bisimulation semantics, that provides a direct symmetric characterisation of it as an equivalence relation, without using any order as intermediate concept. Besides, we have found that it is not necessary to start from a simulation based semantics to get an equivalent global bisimulation. What has proved to be very useful is the axiomatic characterisation of the semantics. Following these ideas we have got also global bisimulation for several semantics, including refusals and traces. That provides a general framework that allows to relate both intensional and extensional semantics.
Lifting Non-Finite Axiomatizability Results to Extensions of Process Algebras
This paper presents a general technique for obtaining new results pertaining to the non-finite axiomatizability of behavioural (pre)congruences over process algebras from old ones. The proposed technique is based on a variation on the classic idea of reduction mappings. In this setting, such reductions are translations between languages that preserve sound (in)equations and (in)equational provability over the source language, and reflect families of (in)equations responsible for the non-finite axiomatizability of the target language.