Abstract
The article investigates fairness and conspiracy in a probabilistic framework, based on unfoldings of Petri nets. Here, the unfolding semantics uses a new, cluster-based view of local choice. The algorithmic construction of the unfolding proceeds on two levels, choice of steps inside conflict clusters, where the choice may be fair or unfair, and the policy controlling the order in which clusters may act; this policy may or may not conspire, e.g., against a transition. In the context of an example where conspiracy can hide in the partial order behavior of a life and 1-safe Petri net, we show that, under non-degenerate i.i.d. randomization on both levels, both conspiracy and unfair behavior have probability 0. The probabilistic model, using special Gibbs potentials, is presented here in the context of 1-safe nets, but extends to any Petri net.
This work was supported by the MAGDA2 project, RNRT.
This is a preview of subscription content, log in via an institution to check access.
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
M. Ajmone Marsan, G. Balbo, G. Conte, S. Donatelli, and G. Franceschinis. Modeling with Generalized Stochastic Petri Nets. Wiley, 1995.
M. Ajmone Marsan, G. Balbo, G. Chiola, and G. Conte. Generalized Stochastic Petri Nets Revisited: Random Switches and Priorities. In: Proceedings of PNPM’87, IEEE-CS Press, pp. 44–53.
A. Aghasaryan, E. Fabre, A. Benveniste, R. Boubour, and C. Jard. Fault detection and diagnosis in distributed systems: An approach by partially stochastic petri nets. Discrete event dynamic systems 8:203–231, 1998.
L. de Alfaro. From Fairness to Chance. In: Electronic Notes on Theoretical Computer Science 22, Elsevier, 2000.
L. de Alfaro. Stochastic Transition Systems. In: CONCUR’98, LNCS 1466:423–438, Springer-Verlag, 1998.
K.R. Apt, N. Francez, and S. Katz. Appraising fairness in languages for distributed programming. Distributed Computing 2:226–241, 1988.
K.R. Attie, N. Francez, and O. Grumberg. Fairness and hyperfairness in multi-parti interactions. Distributed Computing 6:245–254, 1993.
A. Benveniste, S. Haar, and E. Fabre. Markov Nets: probabilistic Models for Distributed and Concurrent Systems. INRIA Report 4235, 2001.
E. Best. Fairness and Conspiracies. Information Processing Letters 18(4):215–220, 1984. Erratum ibidem 19:162.
K. L. Chung. A Course in Probability Theory. Academic Press, 1974.
C. Derman. Finite State Markovian Decision Processes. Acad. Press, 1970.
J. Desel and J. Esparza. Free Choice Petri Nets. Camb. Univ. Press, 1995.
R. Dobrushin. The description of a random field by means of conditional probabilities and conditions of its regularity. Th. Prob. Appl. 13:197–224, 1968.
S. Dolev, A. Israeli, and S. Moran. Analyzing expected time by scheduler-luck games. IEEE Trans on Par. and Dist. Systems, 8(4):424–440, 1997.
J. Engelfriet. Branching Processes of Petri Nets. Acta Inf. 28:575–591, 1991.
J. Esparza, S. Römer, and W. Vogler. An Improvement of McMillan’s Unfolding Algorithm. In: TACAS’96, LNCS 1055:87–106, Springer 1996. Extended version to appear in Formal Methods in System Design.
J. Esparza. Model Checking Using Net Unfoldings. Science of Computer Programming 23:151–195, 1994.
N. Francez. Fairness. Springer, 1986.
S. Haar. Branching Processes of general S/T-Systems. Electronic Notes in Theoretical Computer Science 18, 1998.
S. Haar. Occurrence Net Logics. Fund. Informaticae 43:105–127, 2000.
S. Haar. Clusters, confusion and unfoldings. Fund.Informaticae 47(3-4):259–270, 2001.
S. Haar. Probabilistic Cluster Unfoldings for Petri Nets. INRIA Research Report 4426, 2002; http://www.inria.fr/rrrt/rr-4426.html; ftp://ftp.inria.fr/INRIA/publication/RR/RR-4426.ps.gz
M. Jaeger. Fairness, Computable Fairness and Randomness. PROBMIV’99, Tech. Report CSR-99-8, School of CS, Univ. of Birmingham 1999.
R. Kindermann and J. L. Snell. Markov Random Fields and their Applications. AMS Contemporary Mathematics Vol. 1, Providence 1980.
M. Kwiatkowska. Event fairness and non-interleaving concurrency. Formal Aspects of Computing 1:213–228, 1989.
K. McMillan. Using Unfoldings to avoid the state explosion problem in the verification of asynchronous circuits. 4th CAV, pp. 164–174, 1992.
M. Nielsen, G. Plotkin, and G. Winskel. Petri nets, event structures, and domains. Part I. Theoretical Computer Science 13:85–108, 1981.
M.O. Rabin. Probabilistic Automata. Inf. and Control 6:230–245, 1963.
G. Rozenberg and J. Engelfriet. Elementary Net Systems. In: Lectures on Petri Nets I: Basic Models. LNCS 1491, pp. 12–121, Springer, 1998.
R. Segala. Verification of Randomized Distributed Algorithms. In: LNCS 2090:232–260, Springer 2001.
H. Völzer. Randomized non-sequential processes. In: Proc. CONCUR 2001. LNCS 2154, Springer, August 2001.
W. Vogler. Fairness and Partial Order Semantics. Inf. Proc. Letters 55(1): 33–39, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Haar, S. (2002). Probabilistic Unfoldings and Partial Order Fairness in Petri Nets. In: Hermanns, H., Segala, R. (eds) Process Algebra and Probabilistic Methods: Performance Modeling and Verification. PAPM-PROBMIV 2002. Lecture Notes in Computer Science, vol 2399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45605-8_7
Download citation
DOI: https://doi.org/10.1007/3-540-45605-8_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43913-4
Online ISBN: 978-3-540-45605-6
eBook Packages: Springer Book Archive