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Relational structures model of concurrency

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Abstract

The paper deals with the foundations of concurrency theory. We show how structurally complex concurrent behaviours can be modelled by relational structures \({(X, \diamondsuit, \sqsubset)}\) , where X is a set (of event occurrences), and \({\diamondsuit}\) (interpreted as commutativity) and \({\sqsubset}\) (interpreted as weak causality) are binary relations on X. The paper is a continuation of the approach initiated in Gaifman and Pratt (Proceedings of LICS’87, pp 72–85, 1987), Lamport (J ACM 33:313–326, 1986), Abraham et al. (Semantics for concurrency, workshops in computing. Springer, Heidelberg, pp 311–323, 1990) and Janicki and Koutny (Lect Notes Comput Sci 506:59–74, 1991), substantially developed in Janicki and Koutny (Theoretical Computer Science 112:5–52, 1993) and Janicki and Koutny (Acta Informatica 34:367–388, 1997), and recently generalized in Guo and Janicki (Lect Notes Comput Sci 2422:178–191, 2002) and Janicki (Lect Notes Comput Sci 3407:84–98, 2005). For the first time the full model for the most general case is given.

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  1. Department of Computing and Software, McMaster University, Hamilton, ON, L8S 4K1, Canada

    Ryszard Janicki

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  1. Ryszard Janicki
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Partially supported by NSERC of Canada Grant.

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Janicki, R. Relational structures model of concurrency. Acta Informatica 45, 279–320 (2008). https://doi.org/10.1007/s00236-008-0071-6

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