Abstract
When dealing with process calculi and automata which express both nondeterministic and probabilistic behavior, it is customary to introduce the notion of scheduler to resolve the nondeterminism. It has been observed that for certain applications, notably those in security, the scheduler needs to be restricted so not to reveal the outcome of the protocol’s random choices, or otherwise the model of adversary would be too strong even for “obviously correct” protocols. We propose a process-algebraic framework in which the control on the scheduler can be specified in syntactic terms, and we show how to apply it to solve the problem mentioned above. We also consider the definition of (probabilistic) may and must preorders, and we show that they are precongruences with respect to the restricted schedulers. Furthermore, we show that all the operators of the language, except replication, distribute over probabilistic summation, which is a useful property for verification.
This work has been partially supported by the INRIA DREI Équipe Associée PRINTEMPS and by the INRIA ARC project ProNoBiS.
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
Vardi, M.: Automatic verification of probabilistic concurrent finite-state programs. In: Proc. of the Symp. on Foundations of Comp. Sci., pp. 327–338. IEEE Computer Society Press, Los Alamitos (1985)
Hansson, H., Jonsson, B.: A framework for reasoning about time and reliability. In: Proceedings of the Symp. on Real-Time Systems, pp. 102–111. IEEE Computer Society Press, Los Alamitos (1989)
Yi, W., Larsen, K.: Testing probabilistic and nondeterministic processes. In: Proc. of the IFIP Symp. on Protocol Specification, Testing and Verification (1992)
Segala, R.: Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, MIT/LCS/TR-676 (1995)
Segala, R., Lynch, N.: Probabilistic simulations for probabilistic processes. Nordic Journal of Computing 2(2), 250–273 (1995)
Hansson, H., Jonsson, B.: A calculus for communicating systems with time and probabitilies. In: Proc. of the Real-Time Systems Symp., pp. 278–287. IEEE Computer Society Press, Los Alamitos (1990)
Bandini, E., Segala, R.: Axiomatizations for probabilistic bisimulation. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 370–381. Springer, Heidelberg (2001)
Andova, S.: Probabilistic process algebra. PhD thesis, TU Eindhoven (2002)
Mislove, M., Ouaknine, J., Worrell, J.: Axioms for probability and nondeterminism. In: Proc. of EXPRESS. ENTCS, vol. 96, pp. 7–28. Elsevier, Amsterdam (2004)
Palamidessi, C., Herescu, O.: A randomized encoding of the π-calculus with mixed choice. Theoretical Computer Science 335(2-3), 373–404 (2005)
Deng, Y., Palamidessi, C., Pang, J.: Compositional reasoning for probabilistic finite-state behaviors. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds.) Processes, Terms and Cycles: Steps on the Road to Infinity. LNCS, vol. 3838, pp. 309–337. Springer, Heidelberg (2005)
Sokolova, A., de Vink, E.: Probabilistic automata: system types, parallel composition and comparison. In: Baier, C., Haverkort, B., Hermanns, H., Katoen, J.-P., Siegle, M. (eds.) Validation of Stochastic Systems. LNCS, vol. 2925, pp. 1–43. Springer, Heidelberg (2004)
Jonsson, B., Larsen, K., Yi, W.: Probabilistic extensions of process algebras. In: Handbook of Process Algebra, pp. 685–710. Elsevier, Amsterdam (2001)
Chatzikokolakis, K., Palamidessi, C.: A framework for analyzing probabilistic protocols and its application to the partial secrets exchange. In: De Nicola, R., Sangiorgi, D. (eds.) TGC 2005. LNCS, vol. 3705, pp. 146–162. Springer, Heidelberg (2005)
Canetti, R., Cheung, L., Kaynar, D., Liskov, M., Lynch, N., Pereira, O., Segala, R.: Task-structured probabilistic i/o automata. In: Proc. of WODES (2006)
Canetti, R., Cheung, L., Kaynar, D., Liskov, M., Lynch, N., Pereira, O., Segala, R.: Time-bounded task-PIOAs: A framework for analyzing security protocols. In: Dolev, S. (ed.) DISC 2006. LNCS, vol. 4167, pp. 238–253. Springer, Heidelberg (2006)
Garcia, F., van Rossum, P., Sokolova, A.: Probabilistic anonymity and admissible schedulers, arXiv:0706.1019v1 (2007)
de Alfaro, L., Henzinger, T., Jhala, R.: Compositional methods for probabilistic systems. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, Springer, Heidelberg (2001)
De Nicola, R., Hennessy, M.: Testing equivalences for processes. Theoretical Computer Science 34(1-2), 83–133 (1984)
Abadi, M., Gordon, A.: A calculus for cryptographic protocols: The spi calculus. Information and Computation 148(1), 1–70 (1999)
Chaum, D.: The dining cryptographers problem: Unconditional sender and recipient untraceability. Journal of Cryptology 1, 65–75 (1988)
Bhargava, M., Palamidessi, C.: Probabilistic anonymity. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 171–185. Springer, Heidelberg (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chatzikokolakis, K., Palamidessi, C. (2007). Making Random Choices Invisible to the Scheduler . In: Caires, L., Vasconcelos, V.T. (eds) CONCUR 2007 – Concurrency Theory. CONCUR 2007. Lecture Notes in Computer Science, vol 4703. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74407-8_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-74407-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74406-1
Online ISBN: 978-3-540-74407-8
eBook Packages: Computer ScienceComputer Science (R0)