On causality observed incrementally, finally

  • Gian-Luigi Ferrari
  • Ugo Montanari
  • Miranda Mowbray
CAAP Colloquium On Trees In Algebra And Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 493)


One of the main problems of the partial ordering approach to the description of computations of concurrent and distributed systems is that there is no operation of sequential composition for partial orders which preserves all information on causal dependencies (except for the simple case of series parallel pomsets). As a result, truly concurrent behavioural equivalences are defined by giving integral descriptions of computations: they are not obtained by composing the observations of the elementary steps of the computations. In this paper we introduce the algebra of Concatenable Concurrent Histories. A Concatenable Concurrent History describes a computation by means of a partial ordering of events together with information on the initial and final state of the computation. The operation of sequential conposition is one of the primitive operations of this algebra. We introduce a category of transition systems for CCS (called CCS models) and we show that in this category there exists a CCS model which has the structure of Concatenable Concurrent Histories. This object constitutes our model of observations. As a consequence our observations are incremental. The observation mechanism is handled by a labelling construction which is an internal operation of the category of models. Furthermore, we give a bisimulation congruence for CCS, via Concatenable Concurrent History observations, which can be characterized in terms of a final universal property in a suitable subcategory of CCS models. This category also provides a framework in which to interpret a Hennessy-Milner style programming logic which describes properties of the observable behaviour of computations. The equivalence naturally induced by the logic coincides with the congruence induced by the final object. This result expresses a sort of duality between semantic analysis based on observations and programming logics. We obtain an analogous result for a weaker congruence which results when internal actions are unobservable.


Operational Semantic Congruence Class Communicate Sequential Process Minimal Realization Causal Dependency 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Gian-Luigi Ferrari
    • 1
  • Ugo Montanari
    • 2
  • Miranda Mowbray
    • 3
  1. 1.IEI CNRPisaItaly
  2. 2.Dipartimento di InformaticaUniversità di PisaPisaItaly
  3. 3.Hewlett-Packard Science CentrePisaItaly

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