an:05306283
Zbl 1147.68054
Janicki, Ryszard
Relational structures model of concurrency
EN
Acta Inf. 45, No. 4, 279-320 (2008).
00220145
2008
j
68Q85
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 \textit{H. Gaifman} and \textit{V. Pratt} [``Partial order models of concurrency and the computation of functions'', in: Proceedings of LICS'87, 72--85 (1987)], \textit{L. Lamport} [J. Assoc. Comput. Mach. 33, 313--326 (1986; Zbl 0627.68017)], \textit{U. Abraham, S. Ben-David} and \textit{M. Magodor} [``On global-time and inter-process communication'', in: Semantics for concurrency, Workshops in Computing. Springer, Heidelberg, 311--323 (1990)] and \textit{R. Janicki} and \textit{M. Koutny} [``Invariants and paradigms of concurrency theory'', Lect. Notes Comput. Sci. 506, 59--74 (1991)], substantially developed in [\textit{R. Janicki} and \textit{M. Koutny}, Theor. Comput. Sci. 112, 5--52 (1993; Zbl 0814.68061)] and [\textit{R. Janicki} and \textit{M. Koutny}, Acta Inf. 34, 367--388 (1997; Zbl 0934.68047)], and recently generalized by \textit{G. Guo} and \textit{R. Janicki} [``Modelling concurrent behaviours by commutativity and weak causality relations'', Lect. Notes Comput. Sci. 2422, 178--191 (2002)] and \textit{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.
Zbl 0627.68017; Zbl 0814.68061; Zbl 0934.68047; Zbl 1109.68073