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Relational structures model of concurrency. (English) Zbl 1147.68054
Summary: 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 by H. Gaifman and V. Pratt [“Partial order models of concurrency and the computation of functions”, in: Proceedings of LICS’87, 72–85 (1987)], L. Lamport [J. Assoc. Comput. Mach. 33, 313–326 (1986; Zbl 0627.68017)], U. Abraham, S. Ben-David and M. Magodor [“On global-time and inter-process communication”, in: Semantics for concurrency, Workshops in Computing. Springer, Heidelberg, 311–323 (1990)] and R. Janicki and M. Koutny [“Invariants and paradigms of concurrency theory”, Lect. Notes Comput. Sci. 506, 59–74 (1991)], substantially developed in [R. Janicki and M. Koutny, Theor. Comput. Sci. 112, 5–52 (1993; Zbl 0814.68061)] and [R. Janicki and M. Koutny, Acta Inf. 34, 367–388 (1997; Zbl 0934.68047)], and recently generalized by G. Guo and R. Janicki [“Modelling concurrent behaviours by commutativity and weak causality relations”, Lect. Notes Comput. Sci. 2422, 178–191 (2002)] and R. Janicki [Lect. Notes Comput. Sci. 3407, 84–98 (2005; Zbl 1109.68073)]. For the first time the full model for the most general case is given.

MSC:
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
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