| R.J. van Glabbeek & U. Goltz (1989): Partial order semantics for refinement of actions -- neither necessary nor always sufficient but appropriate when used with care. Bulletin of the European Association for Theoretical Computer Science 38, pp. 154--163. |
....but that partial order semantics is so preserved. The natural computational setting for true concurrency is that of schedules or partially ordered sets of events. If branching time can be moved from automata to schedules [NPW81] can true concurrency go the other way Van Glabbeek and Goltz [vGG89] strengthen the result of Castellano et al. in several ways. First they give a stronger example to show that step semantics (a form of concurrency intermediate between interleaving and partial orders, permitting multiple but synchronized actions at each clock tick) is, like interleaving semantics, ....
....is represented by dimension: an n dimensional cell (element of space) is used to represent the concurrent execution of n sequential processes, and its boundaries represent the starting or halting of some of those processes. Our geometric view is closely related on the one hand to ST bisimulation [vGG89], and on the other to C. Papadimitriou s geometrical model for database concurrency control [Pap86, chap.6] Closer still is M. Shields proposal to add higher dimensional transitions to automata [Shi85] which D. Murphy brought to our attention too late for inclusion in the POPL 91 version of ....
R. van Glabbeek and U. Goltz. Partial order semantics for refinement of actions---neither necessary nor always sufficient but appropriate when used with care. Bulletin of the EATCS, 38:154--163, June 1989.
....deadlock. Notes This paper combines and extends the material of [GG a c d e] except for the part in [GG c] on refinement of transitions in Petri nets and the discussion of TCSP like parallel composition in [GG e] An informal presentation of some basic ingredients of this paper appeared as [GG b]. Among others, the treatment of action refinement in stable and non stable event structures is new. The research reported here was supported by Esprit project 432 (METEOR) Esprit Basic Research Action 3148 (DEMON) Sonderforschungsbereich 342 of the TU Munchen, ONR grant N00014 92 J 1974 and the ....
R.J. van Glabbeek & U. Goltz (1989): Partial order semantics for refinement of actions -- neither necessary nor always sufficient but appropriate when used with care. Bulletin of the European Association for Theoretical Computer Science 38, pp. 154--163.
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