Process Equivalences as Global Bisimulations1

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.

1989

In this paper a process is viewed as a labeled graph modulo bisimulation equivalence. Three topics are covered: (i) specification of processes using finite systems of equations over the syntax of process algebra; (ii) inference systems which are complete for proving the equivalence of regular (finite state) processes; (iii) variations of the bisimulation model.

IFIP International Federation for Information Processing, 2008

We present a theoretical framework which allows to define in a uniform way coinductive characterisations of nearly any semantic preorder or equivalence between processes, by means of simulations up-to and bisimulations up-to. In particular, all the semantics in the linear time-branching time spectrum are covered. Constrained simulations, that generalise plain simulations by including a constraint that all the pairs of related processes must satisfy, are the key to obtain such a general framework. We provide a simple axiomatisation of any constrained simulation preorder and also for the corresponding equivalence. These axiomatizations allow us to prove in a uniform way that each constrained simulation preorder (equivalence) defines a class of process preorders (equivalences) which share commons properties, like the possibility of giving coinductive characterisations for all of them, or the existence of a canonical preorder inducing each of these equivalences.

Lecture Notes in Computer Science, 1994

In the literature one can distinguish two main approaches to the definition of observational semantics of algebraic specifications. On one hand, observational semantics is defined using a notion of observational satisfaction for the axioms of a specification and on the other hand one can define observational semantics of a specification by abstraction with respect to an observational equivalence relation between algebras. In this paper we present an analysis and a comparative study of the different approaches in a more general framework which subsumes not only the observational case but also other examples like the bisimulation congruence of concurrent processes. Thereby the distinction between the different concepts of observational semantics is reflected by our notions of behavioural semantics and abstractor semantics. Our main results show that behavioural semantics can be characterized by an abstractor construction and, vice versa, abstractor semantics can be characterized in terms of behaviourai semantics. Hence there exists a duality between both concepts which allows to express each one by each other. As a consequence we obtain a sufficient and necessary condition under which behavioural and abstractor semantics coincide. Moreover, the semantical characterizations lead to proof-theoretic results which show that behavioural theories of specifications can be reduced to standard theories (of some classes of algebras).

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.