Compositionality and bisimulation: a negative result

2013 20th International Symposium on Temporal Representation and Reasoning, 2013

Formal specification languages have a lot of notions in common. They all introduce entities usually called processes, offer similar operators, and most importantly define their operational semantics based on labeled transition systems (LTS). However, each language defines specific synchronizing and/or memory structures. For instance, in CSP, the synchronization is defined between identical events, while in CCS and in synchronization vectors-based views it is defined respectively between complementary events or between possibly different events. In this paper, we aim at capturing some similarities of specification languages by defining a label-based composition formal framework. Firstly, we define a high-level synchronization mechanism in the form of an abstract label structure. We then couple this label structure with several compositional operations and properties. Secondly, we introduce an LTS-based behavioral framework and define a unique LTS composition operator which is reused to define syntactic composition of extended transition systems and a compositional semantics.

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.

DAIMI Report Series, 1993

This thesis is concerned with the verification of concurrent systems modelled by process algebras. It provides methods and techniques for reasoning about temporal properties as described by assertions from an expressive modal logic -- the modal µ-calculus. It describes a compositional approach to model checking, efficient local and global algorithms for model checking finite-state systems, a general local fixed-point finding algorithm, a proof system for model checking infinite-state systems, a categorical completeness result for an intuitionistic version of the modal µ-calculus, and finally it shows some novel applications of the logic for expressing behavioural 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.

Electronic Notes in Theoretical Computer Science, 2009

The complexity of parallel systems has produced a large collection of semantics for processes, a classification of which is provided by Van Glabbeek's linear time-branching time spectrum; however, no suitable unified definitions were available. We have discovered the way to unify them, both in an observational framework and by means of a quite small set of parameterized (in)equations that provide a sound and complete axiomatization of the preorders that define them. In more detail, we have proved that we only need a generic simulation axiom (NS), which defines the family of constrained simulation semantics, thus covering the class of branching time semantics, and a generic axiom (ND) for reducing the non-determinism of processes, by means of which we introduce the additional identifications induced by each of the linear time semantics.

Electronic Proceedings in Theoretical Computer Science, 2011

We continue with the task of obtaining a unifying view of process semantics by considering in this case the logical characterization of the semantics. We start by considering the classic linear timebranching time spectrum developed by R.J. van Glabbeek. He provided a logical characterization of most of the semantics in his spectrum but, without following a unique pattern. In this paper, we present a uniform logical characterization of all the semantics in the enlarged spectrum. The common structure of the formulas that constitute all the corresponding logics gives us a much clearer picture of the spectrum, clarifying the relations between the different semantics, and allows us to develop generic proofs of some general properties of the semantics.

Software: Practice and Experience, 1992

LOTOS is one of the most recent formal description languages to appear and one of very few with a standard definition. It has both a process algebra and an abstract data-type component, and these facilities are used in combination to describe the behaviour of concurrent systems. The purpose of this paper is to examine, in a tutorial style, what is involved in constructing and taking benefit from such descriptions. The presentation is illustrated through the development of two formal descriptions for the children's game of pass-the-parcel. These descriptions and a concise summary of the main features of LOTOS are given as appendices. Many of the points made in the paper apply equally well to other process-oriented languages such as CCS and CSP.

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.

2000

When verifying concurrent systems described by transition systems, state explosion is one of the most serious problems. If quantitative temporal information (expressed by clock ticks) is considered, state explosion is even more serious. We present a notion of abstraction of transition systems, where the abstraction is driven by the formulae of a quantitative temporal logic, called qu-mu-calculus, defined in the paper. The abstraction is based on a notion of bisimulation equivalence, called ρ, n -equivalence, where ρ is a set of actions and n is a natural number. It is proved that two transition systems are ρ, n -equivalent iff they give the same truth value to all qu-mu-calculus formulae such that the actions occurring in the modal operators are contained in ρ, and with time constraints whose values are less than or equal to n. We present a non-standard (abstract) semantics for a timed process algebra able to produce reduced transition systems for checking formulae. The abstract semantics, parametric with respect to a set ρ of actions and a natural number n, produces a reduced transition system ρ, nequivalent to the standard one. A transformational method is also defined, by means of which it is possible to syntactically transform a program into a smaller one, still preserving ρ, n -equivalence.

Journal of Universal Computer …, 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.