Distributed bisimulations

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A Modal Characterisation of Distributed Bisimulation

In this paper we consider the distributed bisimulation equivalence defined by Hennessy and Castellani and later developed by Castellani. We present a logic in the style of Hennessy-Milner logic to charaterize the equivalence, i.e. we seek a logic such that whenever two processes are distributed bisimulation equivalent, they satisfy the same set of formulae and vice versa. Furthermore, for a small subset of CCS we provide a proof system which is shown to be sound and complete. The proof system is structural both in the structure of formulae and in the structure of processes. For the case of parallel composition of processes we present inference rules defined via a new combinator introduced. The combinator in question is left merge, a special kind of parallel composition in which the left operand has precedence over the other and must perform the first action observed

A Distribution Law for CCS and a New Congruence Result for the pi-calculus

We give an axiomatisation of strong bisimilarity on a small fragment of CCS that does not feature the sum operator. This axiomatisation is then used to derive congruence of strong bisimilarity in the finite pi-calculus in absence of sum. To our knowledge, this is the only nontrivial subcalculus of the pi-calculus that includes the full output prefix and for which strong bisimilarity is a congruence.Comment: 20 page

Distributed CCS

In this paper we describe a technique to extend a process language such as CCS which does not model many aspects of distributed computation to one which does. The idea is to use a concept of location which represents a virtual node. Processes at different locations can evolve independently. Furthermore, communication between the processes at different locations occurs via explicit message passing. We extend CCS with locations and message passing primitives and present its operational semantics. We show that the equivalences induced by the new semantics and its properties are similar to the equivalences in CCS. We also show how the semantics of configuration and routing can be handled

New Bisimulation Semantics for Distributed Systems

Bisimulation semantics are a very pleasant way to define the semantics of systems, mainly because the simplicity of their definitions and their nice coalgebraic properties. However, they also have some disadvantages: they are based on a sequential operational semantics defined by means of an ordinary transition system, and in order to be bisimilar two systems have to be “too similar”. In this work we will present several natural proposals to define weaker bisimulation semantics that we think properly capture the desired behaviour of distributed systems. The main virtue of all these semantics is that they are real bisimulation semantics, thus inheriting most of the good properties of bisimulation semantics. This is so because they can be defined as particular instances of Jacobs and Hughes’ categorical definition of simulation, which they have already proved to satisfy all those properties

Location equivalence in a parametric setting

AbstractLocation equivalence has been presented in [5] as a bisimulation-based equivalence able to take into account the spatial distribution of processes.In this work, the parametric approach of [12] is applied to location equivalence. An observation domain for localities is identified and the associated equivalence is shown to coincide with the equivalence introducted in [6,16]. The observation of a computation is a forest (defined up to isomorphism) whose nodes are the events (labeled by observable actions) and where the arcs describe the sublocation relation.We show in the paper that our approach is really parametric. By performing minor changes in the definitions, many equivalences are captured: partial and mixed ordering causal semantics, interleaving, and a variation of location equivalence where the generation ordering is not evidenced. It seems difficult to modify the definitions of [6,16] to obtain the last observation. The equivalence induced by this observation corresponds to the very intuitive assumption that different locations cannot share a common clock, and hence the ordering between events occurring in different places cannot be determined.Thanks to the general results proved in [12] for the parametric approach, all the observation equivalences described in this paper come equipped with sound and complete axiomatizations

Multiset Bisimulations as a Common Framework for Ordinary and Probabilistic Bisimulations

Our concrete objective is to present both ordinary bisimulations and probabilistic bisimulations in a common coalgebraic framework based on multiset bisimulations. For that we show how to relate the underlying powerset and probabilistic distributions functors with the multiset functor by means of adequate natural transformations. This leads us to the general topic that we investigate in the paper: a natural transformation from a functor F to another G transforms F-bisimulations into G-bisimulations but, in general, it is not possible to express G-bisimulations in terms of F-bisimulations. However, they can be characterized by considering Hughes and Jacobs’ notion of simulation, taking as the order on the functor F the equivalence induced by the epi-mono decomposition of the natural transformation relating F and G. We also consider the case of alternating probabilistic systems where non-deterministic and probabilistic choices are mixed, although only in a partial way, and extend all these results to categorical simulations

True concurrency can be traced

In this paper sets of labelled partial orders are employed as fundamental mathematical entities for modelling nondeterministic and concurrent processes thereby obtaining so-called noninterleaving semantics. Based on closures of sets of labelled partial orders, a simple algebraic language with refinement is given denotational models fully abstract w.r.t. corresponding behaviourally motivated equivalences