Abstract
We present an extension of Milner's CCS [Mil89] with interval time. The notion of time is introduced in terms of time intervals which specify when actions are allowed to occur. We define three equivalences: strong, timed weak, and weak bisimulation equivalence. The strong bisimulation equivalence refines the corresponding relation in CCS by requiring strongly bisimilar processes to have the same timing behavior, the weak bisimulation equivalence is in essence the weak bisimulation equivalence of CCS, while the timed weak equivalence lays strictly between strong and weak equivalence, since it in addition to weak bisimularity also considers the timing of observable actions.
We define a refinement relation for processes specified in our calculus, which can be used to order processes according to their real-time behavior. This relation can be interpreted as “having a more precise timing specification than”. For example, the refinement relation can be used to show that an implementation (which normally has more precise time requirements) meets an abstract specification in which the time requirements are specified more generously.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
J.C.M. Baeten & J.A. Bergstra, ‘Real Time Process Algebra', Report P8916, University of Amsterdam Programming Research Group, 1989
K.A. Bartlett, R.A. Scantlebury, P.T. Wilkinson, ‘A note on reliable full-duplex transmission over halfduplex links', Communications of the ACM, Vol 12, No 5, pp 260–261, 1969
M. Daniels, ‘CCS with Interval Time', DoCS 91/32, Department of Computer Systems, Uppsala University, 1991
J.F. Groote & F. Vaandrager, 'structured operational semantics and bisimulation as a congruence', CSR8845, Centre for Mathematics and Computer Science, dept of Computer Science, 1988
H. Hansson, ‘Time and Probability in Formal Design of Distributed Systems', PhD thesis DoCS 91/27, Department of Computer Systems, Uppsala University, 1991
C. Hoare, ‘Communicating sequential processes'. Communications of the ACM, Vol 21, No 8, pp 666–677, ACM, 1978
R. Milner, Communication and Concurrency, Prentice Hall, 1989
F. Moller & C. Tofts, ‘A temporal calculus of communicating systems', Proc. CONCUR '90, LNCS 458, pp 401–415, Springer Verlag 1990
X. Nicollin, J. Richier, J. Sifakis, & J. Voiron, ‘ATP: an algebra for timed processes', Technical report RT-C16, IMAG, Grenoble, 1990
X. Nicollin & J. Sifakis, ‘The algebra of timed processes ATP: an algebra for timed processes', Technical report RT-C26, IMAG, Grenoble, 1990
G. Plotkin, ‘A structural approach to operating semantics', FN 19, DAIMI, Aarhus University, Denmark, 1981
G. Reed & A. Roscoe, ‘A timed model for communicating sequential processes', Proc 13th ICALP, LNCS Vol 226, pp 314–323, 1986
S. Schneider, ‘Correctness and Communication in Real-Time Systems', PhD thesis technical monograph PRG-84, Oxford University Computing Laboratory, Oxford UK, 1989
Y. Wang, ‘CCS + time = an interleaving model for real time systems', Proc. ICALP '91, to appear in LNCS 510, pp 217–228, Springer Verlag 1991
Author information
Authors and Affiliations
Corresponding author
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Daniels, M. (1991). Modelling real-time behavior with an interval time calculus. In: Vytopil, J. (eds) Formal Techniques in Real-Time and Fault-Tolerant Systems. FTRTFT 1992. Lecture Notes in Computer Science, vol 571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55092-5_4
Download citation
DOI: https://doi.org/10.1007/3-540-55092-5_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55092-1
Online ISBN: 978-3-540-46692-5
eBook Packages: Springer Book Archive