Abstract
In 1959, Muller and Bartky published a celebrated paper on “A Theory of Asynchronous Circuits”. Among many novel techniques in that paper was the use of lattices resembling the domains of configurations of event structures. In the light of this we present a generalization of Muller's construction to safe nets. We find, however, that this “Müller unfolding” cannot be generated as the domain of configurations of any known event structure, not even a General Event Structure. (In particular, this unfolding differs from that of Nielsen, Plotkin and Winskel.) This paper attempts to fill that gap. We make use of the logical approach to causality in which a General Event Structure is interpreted as a “logical automaton” arising from a particular logic of causality. We introduce a new causal logic and associate a corresponding logical automaton to any finite safe Petri net. Our main result is that the domain of configurations of this generalized event structure is isomorphic to the Muller unfolding of the net.
Preview
Unable to display preview. Download preview PDF.
References
J. A. Brzozowski and C.-J. H. Seger. Advances in Asynchronous Circuit Theory Part I: gate and unbounded inertial delay models. Bulletin of the EATCS, 42:198–249, 1990.
M. Droste. Event structures and domains. Theoretical Computer Science, 68:37–47, 1989.
J. Gunawardena. Events, Causality and Logic. In preparation.
J. Gunawardena. Geometric logic, causality and event structures. In J. C. M. Baeten and J. F. Groote, editors, CONCUR'91 — 2nd International Conference on Concurrency Theory, pages 266–280. Springer LNCS 527, 1991.
J. Gunawardena. Causal Automata. Theoretical Computer Science, 101:265–288, 1992.
J. Gunawardena. On the causal structure of the Muller unfolding. Technical Report STAN-CS-93-1466, Department of Computer Science, Stanford University, March 1993.
P. T. Johnstone. Stone Spaces, volume 3 of Studies in Advanced Mathematics. Cambridge University Press, 1982.
L. H. Landweber and E. L. Robertson. Properties of Conflict-Free and Persistent Petri Nets. Journal ACM, 25(3):352–364, 1978.
D. E. Muller and W. S. Bartky. A theory of asynchronous circuits. In Proceedings of an International Symposium on the Theory of Switching. Harvard University Press, 1959.
M. Nielsen, G. Plotkin, and G. Winskel. Petri nets, event structures and domains. Theoretical Computer Science, 13:85–108, 1981.
R. J. Parikh. On context-free languages. Journal ACM, 13(4):570–581, 1966.
W. Reisig. Petri Nets, volume 4 of EATCS Monographs on Theoretical Computer Science. Springer-Verlag, 1985.
S. Vickers. Topology via Logic, volume 5 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1989.
G. Winskel. Event structures. In W. Brauer, W. Reisig, and G. Rozenberg, editors, Advances in Petri Nets. Springer LNCS 255, 1987.
A. Yakovlev. Analysing Concurrent Systems through Lattices. Draft, 1991.
A. Yakovlev, L. Lavagno, and A. Sangiovanni-Vincentelli. A Unified Signal Transition Graph Model for Asynchronous Control Circuit Synthesis. In Proceedings ICCAD'92, 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gunawardena, J. (1993). A generalized event structure for the Muller unfolding of a safe net. In: Best, E. (eds) CONCUR'93. CONCUR 1993. Lecture Notes in Computer Science, vol 715. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57208-2_20
Download citation
DOI: https://doi.org/10.1007/3-540-57208-2_20
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57208-4
Online ISBN: 978-3-540-47968-0
eBook Packages: Springer Book Archive