Abstract
We address the problem of characterizing fair (infinite) behaviours of concurrent systems as limits of finite approximations. The framework chosen is Milner's Calculus of Communicating Systems. The results can be summarized as follows. On the set FD of all finite derivations in the calculus we define three distances: da, dw, ds. Then the metric completion of (FD,da) yields the space of all derivations, while the completion of (FD,dw), resp. (FD,ds), yields the space of all finite derivations together with all — and only — the weakly, resp. strongly, fair computations (i.e. non-extendable derivations). The results concerning da and dw are a reformulation of previously known ones, while that concerning ds is — we believe — new.
This research was carried out while the author was at the Dept. of Computer Science of the University of Edinburgh.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
A. ARNOLD, M. NIVAT. Metric interpretations of infinite trees and semantics of non-deterministic recursive procedures. T.C.S. 11 (1980) 181–205.
J.W. DE BAKKER, J.I. ZUCKER. Processes and a fair semantics for the ADA rendez-vous. ICALP'83, LNCS 154 (1983) 52–66.
G. COSTA. A metric characterization of fair computations in CCS. Technical Rep. CSR-169-84, Dept. Comput. Sci. Univ. Edinburgh (1984).
G. COSTA, C. STIRLING. A fair calculus of communicating systems. To appear in Acta Informatica; shortened version: FCT'83, LNCS 158 (1983) 94–105.
G. COSTA, C. STIRLING. Weak and strong fairness in CCS. Technical Rep. CSR-167-84, Dept. Comput. Sci. Univ. Edinburgh (1984); shortened version: MFCS'84, LNCS 176 (1984) 245–254.
P. DEGANO, U. MONTANARI. Liveness properties as convergence in metric spaces. Proc. 16th ACM STOC (1984).
M. HENNESSY. Private communication.
R. MILNER. A calculus of communicationg systems. LNCS 92 (1980).
R. MILNER. A finite delay operator in synchronous CCS. Technical Rep. CSR-116-82 Dept. Comput. Sci. Univ. Edinburgh (1982).
D. PARK. On the semantics of fair parallelism. LNCS 86 (1980) 504–526.
D. PARK. A predicate transformer for weak fair iteration. Proc. 6th IBM Symp. on Mathematical Foundat. of Comput. Sci., Hakone, Japan (1981).
D. PARK. The "fairness" problem and nondeterministic computing networks. Foundat. of Comput. Sci. IV, De Bakker — Van Leuven edit. Amsterdam (1982).
G. PLOTKIN. A powerdomain for countable nondeterminism. ICALP'82, LNCS 140 (1982) 418–482.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Costa, G. (1985). A metric characterization of fair computations in CCS. In: Ehrig, H., Floyd, C., Nivat, M., Thatcher, J. (eds) Mathematical Foundations of Software Development. CAAP 1985. Lecture Notes in Computer Science, vol 185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15198-2_15
Download citation
DOI: https://doi.org/10.1007/3-540-15198-2_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15198-2
Online ISBN: 978-3-540-39302-3
eBook Packages: Springer Book Archive