Abstract
In prime event structures with binary conflicts (pes-bc) a branching cell [1] is a subset of events closed under downward causality and immediate conflict relations. This means that no event outside the branching cell can be in conflict with or enable any event inside the branching cell. It bears a strong resemblance to stubborn sets, a partial order reduction method on transition systems. A stubborn set (at a given state) is a subset of actions such that no execution consisting entirely of actions outside the stubborn set can be in conflict with or enable actions that are inside the stubborn set.
A rigorous study of the relationship between the two ideas, however, is not straightforward due to the facts that 1) stubborn sets utilise sophisticated causality and conflict relations that invalidate the stability and coherence of event structures [18], 2) without stability it becomes very difficult to define concepts like prefixes and branching cells, which prerequire a clear notion of causality, and 3) it is challenging to devise a technique for identifying ‘proper’ subsets of transitions as ‘events’ such that the induced event-based system captures exactly the causality and conflict information needed by stubborn sets.
In this paper we give a solution to the problems by providing an unfolding of labelled transition systems into configuration structures, a more general structure supporting or-causality and finite conflict. We show that the branching cell definition can be extended to configuration structures and that each branching cell in the unfolding is a long-lived stubborn set, such that no matter how the system evolves, what remains of the branching cell is always a stubborn set.
Supported by the PEARL project (041/2007/A3) from FDCT (Macau).
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
Abbes, S., Benveniste, A.: True-concurrency probabilistic models: Branching cells and distributed probabilities for event structures. Information and Computation 204(2), 231–274 (2006)
Clarke, E.M., Grumberg, O., Minea, M., Peled, D.: State space reduction using partial order techniques. STTT 2(3), 279–287 (1999)
Godefroid, P.: Partial-Order Methods for the Verification of Concurrent Systems. LNCS, vol. 1032. Springer, Heidelberg (1996)
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)
Liu, X., Walker, D.: Partial confluence of proceses and systems of objects. TCS 206(1-2), 127–162 (1998)
Mazurkiewicz, A.: Trace theory. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 279–324. Springer, Heidelberg (1987)
Nielsen, M., Plotkin, G., Winskel, G.: Petri nets, event structures and domains. In: Kahn, G. (ed.) Semantics of Concurrent Computation. LNCS, vol. 70, pp. 266–284. Springer, Heidelberg (1979)
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)
Valmari, A.: The state explosion problem. In: Reisig, W., Rozenberg, G. (eds.) APN 1998. LNCS, vol. 1491, pp. 429–528. Springer, Heidelberg (1998)
Valmari, A.: Stubborn set methods for process algebras. In: POMIV 1996. DIMACS Series in DM&TCS, vol. 29, pp. 213–231 (1997)
van Glabbeek, R.J.: History preserving process graphs (1996), http://kilby.stanford.edu/~rvg/pub/history.draft.dvi
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)
Varacca, D., Völzer, H., Winskel, G.: Probabilistic event structures and domains. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 481–496. 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, Oxford (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
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hansen, H., Wang, X. (2011). On the Origin of Events: Branching Cells as Stubborn Sets. In: Kristensen, L.M., Petrucci, L. (eds) Applications and Theory of Petri Nets. PETRI NETS 2011. Lecture Notes in Computer Science, vol 6709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21834-7_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-21834-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21833-0
Online ISBN: 978-3-642-21834-7
eBook Packages: Computer ScienceComputer Science (R0)