Abstract
In this paper we study nets whose boundaries in a context net consist of places only, i.e. nets that communicate asynchronously with their environment. Such nets are called equivalent, if exchanging them in any context preserves deadlock-freeness. We characterize this equivalence internally, i.e. without referring to all possible contexts. Since this equivalence is undecidable in general, we then define a subclass of nets that are to some degree deterministic. For nets from this subclass we can show that the equivalence is decidable and that the exchange of equivalent nets does not only preserve deadlock-freeness, but gives nets that are even bisimilar; these results especially apply to the behaviour preserving refinement of transitions.
This work was partially supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 342: Methoden und Werkzeuge zur Nutzung paralleler Rechnerarchitekturen, TU München and the ESPRIT Basic Research Action No. 3148 DEMON (Design Methods Based on Nets).
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
C. André. The behaviour of a Petri net on a subset of transitions. R.A.I.R.O., 17:5–21, 1983.
B. Baumgarten. On internal and external characterizations of PT-net building block behaviour. In G. Rozenberg, editor, Advances in Petri Nets 1988, Lect. Notes Comp. Sci. 340, 44–61, 1988.
W. Brauer, R. Gold, and W. Vogler. A survey of behaviour and equivalence preserving refinement of petri nets. In G. Rozenberg, editor, Advances in Petri Nets, Lect. Notes Comp. Sci. 483, 1–46, 1991.
S.D. Brookes, C.A.R. Hoare, and A.W. Roscoe. A theory of communicating sequential processes. J. ACM, 31:560–599, 1984.
S.D. Brookes. A model for communicating sequential processes. Technical Report CMU-CS-83-149, Carnegie-Mellon-Univ., Pittsburgh, 1983.
G. Chehaibar. Replacement of open interface subnets and stable state transformation equivalence. In Proc. 12th Int. Conf. Applications and Theory of Petri Nets, Gjern, pages 390–409, 1991.
J. Engelfriet. Determinacy → (observation equivalence = trace equivalence). Theoret, Comput. Sci., 36:21–25, 1985.
R. Milner. Calculi for synchrony and asynchrony. Theor. Comput. Sci., 25:267–310, 1983.
K. Müller. Constructable Petri nets. Elektr. Inf. Kybern., 21:171–199, 1985.
E.R. Olderog and C.A.R. Hoare. Specification-oriented semantics for communicating processes. Acta Informatica, 23:9–66, 1986.
D. Park. Concurrency and automata on infinite sequences. In P. Deussen, editor, Proc. 5th GI Conf. on Theoretical Comp. Sci., Lect. Notes Comp. Sci. 104, 167–183, 1981.
W.C. Rounds and S.D. Brookes. Possible futures, acceptances, refusals and communicating processes. In Proc. 22nd Ann. Symp. on Foundations of Comp. Sci., pages 140–149. IEEE, 1981.
W. Reisig. Petri Nets. EATCS Monographs on Theoretical Computer Science. Springer, 1985.
Y. Souissi. On liveness preservation by composition of nets via a set of places. In Proc. 11th Int. Conf. on Application and Theory of Petri Nets, pages 104–122, 1990.
W. Vogler. Behaviour preserving refinements of Petri nets. In G. Tinhofer and G. Schmidt, editors, Graph-Theoretic Concepts in Computer Science, Proc. WG 86, Bernried, Lect. Notes Comp. Sci. 246, 82–93, 1987.
W. Vogler. Failures semantics and deadlocking of modular Petri nets. Acta Informatica, 26:333–348, 1989.
W. Vogler. Modular Construction and Partial Order Semantics of Petri Nets. Lect. Notes Comp. Sci. Springer, 1992. To appear.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vogler, W. (1992). Asynchronous communication of Petri Nets and the refinement of transitions. In: Kuich, W. (eds) Automata, Languages and Programming. ICALP 1992. Lecture Notes in Computer Science, vol 623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55719-9_108
Download citation
DOI: https://doi.org/10.1007/3-540-55719-9_108
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55719-7
Online ISBN: 978-3-540-47278-0
eBook Packages: Springer Book Archive