Abstract
We propose a denotational model for real time concurrent systems, based on the failures model for CSP. The fixed point theory is based on the Banach fixed point theorem for complete metric spaces, since the introduction of time as a measure makes all recursive operators naturally contractive. This frees us from many of the constraints imposed by partial orders on the treatment of nondeterminism and divergence.
The work reported in this paper was supported by the U.S. Office of Naval Research under grant N0014-85-G-0123.
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5. References
A. Boucher, A time-based model for occam, Oxford University D.Phil. thesis 1986.
S.D. Brookes, A model for communicating sequential processes, Oxford University D.Phil. thesis 1983.
M. Broy, Fixed point theory for communication and concurency, TC2 Working Conference on Formal Description of Programming Concepts II, Garmisch, 1982.
S.D. Brookes, C.A.R. Hoare and A.W. Roscoe, A theory of communicating sequential processes, JACM 31 (1894), 560–599.
S.D. Brookes and A.W. Roscoe, An improved failures model for communicating processes, Proceedings of the Pittsburgh Seminar on Concurrency, Springer LNCS 197 (1985).
J.W. de Bakker and J.I. Zucker, Processes and the denotational semantics of concurrency, Information and Control 54 (1982), 70–120.
W.G. Golson and W.C. Rounds, Connections between two theories of concurrency: metric spaces and synchronisation trees, Information and Control 57 (1983), 102–124.
C.A.R. Hoare, A model for communicating sequential processes, On the construction of programs CUP (1980), 229–248.
C.A.R. Hoare, Communicating sequential processes, Prentice-Hall International, 1985.
G. Jones, A timed model for communicating processes, Oxford University D.Phil thesis, 1982.
R. Koymans, R.K. Shyamasundar, W.P. de Roever, R. Gerth and S. Arun-Kumar, Compositional semantics for real-time distributed computing Faculteit der Wiskunde en Natuurwetenschappen, Katholieke Universiteit, Nijmegen, Technical report 68, 1985.
M. Nivat, Infinite words, infinite trees, infinite computations, Foundations of Computer Science III (Math. Centre Tracts 109, 1979), 3–52.
E.R. Olderog and C.A.R. Hoare, Specification-oriented semantics for communicating processes, Springer LNCS 154 (1983), 561–572.
I. Phillips, Refusal testing, Proceedings of ICALP'86, Springer LNCS 226 (1986), 304–313.
A.W. Roscoe, A mathematical theory of communicating processes, Oxford University D.Phil thesis 1982.
W.C. Rounds, Applications of topology to the semantics of communicating processes, Proceedings of the Pittsburgh Seminar on Concurrency, Springer LNCS 197 (1985).
G.M. Reed and A.W. Roscoe, A timed model for communicating sequential processes, Proceedings of ICALR'86, Springer LNCS 226 (1986), 314–323.
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© 1988 Springer-Verlag Berlin Heidelberg
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Reed, G.M., Roscoe, A.W. (1988). Metric spaces as models for real-time concurrency. In: Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Language Semantics. MFPS 1987. Lecture Notes in Computer Science, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19020-1_17
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DOI: https://doi.org/10.1007/3-540-19020-1_17
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