Abstract
In process semantics of Petri Net, a non-sequential process is a concurrent run of the system represented in a partial order-like structure. For transition systems it is possible to define a similar notion of concurrent run by utilising the idea of confluence. Basically a confluent process is an acyclic confluent transition system that is a partial unfolding of the original system. Given a non-confluent transition system G, how to find maximal confluent processes of G is a theoretical problem having many practical applications.
In this paper we propose an unfolding procedure for extracting maximal confluent processes from transition systems. The key technique we utilise in the procedure is the construction of granular configuration structures (i.e. a form of event structures) based on diamond-structure information inside transition systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Badouel, E., Bernardinello, L., Darondeau, P.: The synthesis problem for elementary net systems is np-complete. Theor. Comput. Sci. 186(1-2), 107–134 (1997)
Best, E., Devillers, R.R.: Sequential and concurrent behaviour in petri net theory. Theor. Comput. Sci. 55(1), 87–136 (1987)
Best, E., Fernández, C.: Nonsequential processes: a Petri net view. EATCS Monographs on TCS, vol. 13. Springer (1988)
Godefroid, P.: Partial-order Methods for the Verification of Concurrent Systems: an Approach to the State-explosion Problem. LNCS, vol. 1032. Springer, Heidelberg (1996)
Goltz, U., Reisig, W.: The non-sequential behavior of petri nets. Information and Control 57(2/3), 125–147 (1983)
Groote, J.F., Sellink, M.P.A.: Confluence for process verification. Theoretical Computer Science 170(1-2), 47–81 (1996)
Gunawardena, J.: Causal automata. TCS 101(2), 265–288 (1992)
Hansen, H., Wang, X.: On the Origin of Events: Branching Cells as Stubborn Sets. In: Kristensen, L.M., Petrucci, L. (eds.) PETRI NETS 2011. LNCS, vol. 6709, pp. 248–267. Springer, Heidelberg (2011)
Liu, X., Walker, D.: Partial confluence of proceses and systems of objects. TCS 206(1-2), 127–162 (1998)
Milner, R.: Concurrency and Communication. Prentice-Hall (1988)
Peled, D.A.: All From One, One For All: On Model Checking Using Representatives. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 409–423. Springer, Heidelberg (1993)
Sassone, V., Nielsen, M., Winskel, G.: Models for concurrency: Towards a classification. Theor. Comput. Sci. 170(1-2), 297–348 (1996)
Valmari, A.: Stubborn Sets for Reduced State Space Generation. In: Rozenberg, G. (ed.) APN 1990. LNCS, vol. 483, pp. 491–515. Springer, Heidelberg (1991)
van Glabbeek, R.J., Plotkin, G.D.: Configuration structures, event structures and petri nets. Theoretical Computer Science 410(41), 4111–4159 (2009)
van Glabbeek, R., Goltz, U.: Refinement of actions and equivalence notions for concurrent systems. Acta Informatica 37(4), 229–327 (2001)
van Glabbeek, R.J., Plotkin, G.D.: Event Structures for Resolvable Conflict. In: Fiala, J., Koubek, V., KratochvÃl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 550–561. Springer, Heidelberg (2004)
Winskel, G.: Event Structures. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 325–392. Springer, Heidelberg (1987)
Winskel, G., Nielsen, M.: Models for concurrency. In: Handbook of Logic in Computer Science, vol. 4. Clarendon Press (1995)
Yakovlev, A., Kishinevsky, M., Kondratyev, A., Lavagno, L., Pietkiewicz-Koutny, M.: On the models for asynchronous circuit behaviour with or causality. FMSD 9(3), 189–233 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, X. (2012). Maximal Confluent Processes. In: Haddad, S., Pomello, L. (eds) Application and Theory of Petri Nets. PETRI NETS 2012. Lecture Notes in Computer Science, vol 7347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31131-4_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-31131-4_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31130-7
Online ISBN: 978-3-642-31131-4
eBook Packages: Computer ScienceComputer Science (R0)