research-article

Probabilistic bisimulation as a congruence

Authors:

Ruggero Lanotte,

Simone TiniAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 10, Issue 2

Article No.: 9, Pages 1 - 48

https://doi.org/10.1145/1462179.1462181

Published: 02 March 2009 Publication History

Abstract

We propose both an SOS transition rule format for the generative model of probabilistic processes, and an SOS transition rule format for the reactive model of the probabilistic processes. Our rule formats guarantee that probabilistic bisimulation is a congruence with respect to process algebra operations. Moreover, our rule format for generative process algebras guarantees that the probability of the moves of a given process, if there are any, sum up to 1, and the rule format for reactive process algebras guarantees that the probability of the moves of a given process labeled with the same action, if there are any, sum up to 1. We show that most operations of the probabilistic process algebras studied in the literature are captured by our formats, which, therefore, have practical applications.

References

[1]

Aceto, L., Fokkink, W. J., and Verhoef, C. 2001. Structural operational semantics. In Handbook of Process Algebra, J. A. Bergstra et al., Eds. Elsevier, Amsterdam, 197--292.

[2]

Aldini, A., Bravetti, M., and Gorrieri, R. 2004. A process-algebraic approach for the analysis of probabilistic non-interference. J. Comput. Secur. 12, 2, 191--245.

Digital Library

[3]

Baeten, J. C. M., Bergstra, J. A., and Smolka, S. A. 1995. Axiomatizing probabilistic processes: ACP with generative probabilities. Inf. Comput. 121, 2, 234--255.

Digital Library

[4]

Baier, C. and Hermanns, H. 1997. Weak bisimulation for fully probabilistic processes. In Proceedings of the International Conference on Computer Aided Verification. Lecture Notes in Computer Science, vol. 1254. Springer, 119--130.

Digital Library

[5]

Bartels, F. 2002. GSOS for probabilistic transition systems. In Coalgebraic Methods in Computer Science. Electronic Notes in Theoretical Computer Science, vol. 65. Elsevier, Amsterdam.

[6]

Bartels, F. 2004. On generalized coinduction and probabilistic specification formats. Ph.D. thesis, Vrije Univesiteit, Amsterdam.

[7]

Bloom, B., Istrail, S., and Meyer, A. 1995. Bisimulation can't be traced. Commun. ACM 42, 1, 232--268.

Digital Library

[8]

Bravetti, M. and Aldini, A. 2003. Discrete time generative-reactive probabilistic processes with different advancing speeds. Theor. Comput. Sci. 290, 1, 355--406.

Digital Library

[9]

D'Argenio, P. R., Hermanns, H., and Katoen, J. P. 1999. On generative parallel composition. In Proceedings of the International Workshop on Probabilistic Methods in Verification. Electronic Notes in Theoretical Computer Science, vol. 22. Elsevier, Amsterdam.

[10]

de Simone, R. 1985. Higher-Level synchronizing devices in meije-sccs. Theor. Comput. Sci. 37, 245--267.

[11]

Giacalone, A., Jou, C. C., and Smolka, S. A. 1990. Algebraic reasoning for probabilistic concurrent systems. In Proceedings of the IFIP Working Conference on Programming, Concepts and Methods. North Holland, 443--458.

[12]

Groote, J. F. 1993. Transition system specification with negative premises. Theor. Comput. Sci. 118, 2, 263--299.

Digital Library

[13]

Groote, J. F. and Vaandrager, F. 1992. Structured operational semantics and bisimulation as a congruence. Inf. Comput. 100, 2, 202--260.

Digital Library

[14]

Jonsson, B., Larsen, K. G., and Yi, W. 2001. Probabilistic extensions of process algebras. In Handbook of Process Algebra, J. A. Bergstra et al., Eds. Elsevier, Amsterdam, 685--710.

[15]

Kleene, S. C. 1956. Representation of events in nerve nets and finite automata. In Automata Studies, C. E. Shannon and J. McCarthy, Eds. Princeton University Press, Princeton, NJ, 3--41.

[16]

Lanotte, R. and Tini, S. 2005. Probabilistic congruence for generative semistochastic processes. In Proceedings of the International Conference on Foundations of Software Science and Computation Structures. Lecture Notes in Computer Science, vol. 3441. Springer, 63--78.

Digital Library

[17]

Larsen, K. G. and Skou, A. 1991. Bisimulation trough probabilistic testing. Inf. Comput. 94, 1, 1--28.

Digital Library

[18]

Milner, R. 1991. The polyadic π-calculus: A tutorial. Tech. rep. ECS--LFCS--91--180, Department of Computer Science, Edinburgh University.

[19]

Plotkin, G. 1981. A structural approach to operational semantics. Tech. rep. DAIMI FN-19, University of Aarhus.

[20]

Plotkin, G. 2004. A structural approach to operational semantics. J. Log. Algebr. Program. 60--61, 17--139.

[21]

Stark, E. W. and Smolka, S. A. 1999. A complete axiom system for finite-state probabilistic processes. In Proof, Language and Interaction: Essays in Honor of Robin Milner, G. Plotkin et al., Eds. MIT Press, Cambridge, MA, 571--595.

Digital Library

[22]

Tini, S. 2003. Rule formats for non-interference. In Proceedings of the European Symposium on Programming. Lecture Notes in Computer Science, vol. 2618. Springer, 129--143.

Digital Library

[23]

Tini, S. 2004. Rule formats for compositional non interference properties. J. Log. Algebr. Program. 60--61, 353--400.

[24]

Turi, D. and Plotkin, G. 1997. Towards a mathematical operational semantics. In Proceedings of the IEEE Symposium on Logic in Computer Science. IEEE Press, Los Alamitos, CA, 280--291.

Digital Library

[25]

Ulidowski, I. and Phillips, I. 2002. Ordered SOS process languages for branching and eager bisimulations. Inf. Comput. 178, 1, 180--213.

Digital Library

[26]

Ulidowski, I. and Yuen, S. 2004. Process languages with discrete relative time based on the ordered SOS format and rooted eager bisimulation. J. Log. Algebr. Program. 60--61, 401--460.

[27]

van Glabbeek, R. J. 2004. The meaning of negative premises in transition system specifications ii. J. Log. Algebr. Program. 60-61, 229--258.

[28]

van Glabbeek, R. J., Smolka, S. A., and Steffen, B. 1995. Reactive, generative and stratified models of probabilistic processes. Inf. Comput. 121, 1, 59--80.

Digital Library

[29]

Wu, S. H., Smolka, S. A., and Stark, E. W. 1997. Composition and behaviors of probabilistic i/o automata. Theor. Comput. Sci. 176, 1--2, 1--38.

Digital Library

Cited By

Castiglioni VLanotte RTini S(2024)Back to the format: A survey on SOS for probabilistic processesJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2023.100929137(100929)Online publication date: Feb-2024
https://doi.org/10.1016/j.jlamp.2023.100929
Cimini M(2023)A Declarative Validator for GSOS LanguagesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.378.2378(14-25)Online publication date: 13-Apr-2023
https://doi.org/10.4204/EPTCS.378.2
Castiglioni VTini S(2020)Probabilistic divide & congruenceTheoretical Computer Science10.1016/j.tcs.2019.09.037802:C(147-196)Online publication date: 8-Jan-2020
https://dl.acm.org/doi/10.1016/j.tcs.2019.09.037
Show More Cited By

Index Terms

Probabilistic bisimulation as a congruence
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
      1. Semantics
2. Theory of computation
  1. Models of computation
    1. Concurrency
      1. Parallel computing models
    2. Probabilistic computation
  2. Semantics and reasoning
    1. Program semantics

Recommendations

Congruence kernels of orthomodular implication algebras

Abstracting from certain properties of the implication operation in Boolean algebras leads to so-called orthomodular implication algebras. These are in a natural one-to-one correspondence with families of orthomodular lattices. It is proved that ...
Notes on Generative Probabilistic Bisimulation

In this notes we consider the model of Generative Probabilistic Transition Systems, and Baier and Hermanns' notion of weak bisimulation defined over them. We prove that, if we consider any process algebra giving rise to a Probabilistic Transition System ...
Bisimulation congruence of ℵ-calculus

χ-Calculus was proposed as a process calculus that has a uniform treatment of names. Preliminary properties of χ-calculus have been examined in the literature. In this paper a more systematic study of bisimilarities for χ-processes is carried out. The ...

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 10, Issue 2

February 2009

275 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/1462179

Issue’s Table of Contents

Copyright © 2009 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 02 March 2009

Accepted: 01 October 2007

Revised: 01 July 2007

Received: 01 March 2006

Published in TOCL Volume 10, Issue 2

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article
Research
Refereed

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

24
Total Citations
View Citations
240
Total Downloads

Downloads (Last 12 months)3
Downloads (Last 6 weeks)1

Reflects downloads up to 13 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

Castiglioni VLanotte RTini S(2024)Back to the format: A survey on SOS for probabilistic processesJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2023.100929137(100929)Online publication date: Feb-2024
https://doi.org/10.1016/j.jlamp.2023.100929
Cimini M(2023)A Declarative Validator for GSOS LanguagesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.378.2378(14-25)Online publication date: 13-Apr-2023
https://doi.org/10.4204/EPTCS.378.2
Castiglioni VTini S(2020)Probabilistic divide & congruenceTheoretical Computer Science10.1016/j.tcs.2019.09.037802:C(147-196)Online publication date: 8-Jan-2020
https://dl.acm.org/doi/10.1016/j.tcs.2019.09.037
Castiglioni VTini S(2019)Logical characterization of branching metrics for nondeterministic probabilistic transition systemsInformation and Computation10.1016/j.ic.2019.06.001268(104432)Online publication date: Oct-2019
https://doi.org/10.1016/j.ic.2019.06.001
Gebler DTini S(2018)SOS specifications for uniformly continuous operatorsJournal of Computer and System Sciences10.1016/j.jcss.2017.09.01192:C(113-151)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1016/j.jcss.2017.09.011
van Glabbeek RAceto LIngólfsdóttir A(2017)Lean and full congruence formats for recursionProceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3329995.3330077(1-11)Online publication date: 20-Jun-2017
https://dl.acm.org/doi/10.5555/3329995.3330077
van Glabbeek R(2017)Lean and full congruence formats for recursion2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS.2017.8005142(1-11)Online publication date: Jun-2017
https://doi.org/10.1109/LICS.2017.8005142
Castiglioni VGebler DTini S(2016)Logical Characterization of Bisimulation MetricsElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.227.4227(44-62)Online publication date: 25-Oct-2016
https://doi.org/10.4204/EPTCS.227.4
D'Argenio PGebler DLee M(2016)A general SOS theory for the specification of probabilistic transition systemsInformation and Computation10.1016/j.ic.2016.03.009249:C(76-109)Online publication date: 1-Aug-2016
https://dl.acm.org/doi/10.1016/j.ic.2016.03.009
Lee Mde Vink E(2015)Rooted branching bisimulation as a congruence for probabilistic transition systemsElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.194.6194(79-94)Online publication date: 28-Sep-2015
https://doi.org/10.4204/EPTCS.194.6
Show More Cited By

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Issue’s Table of Contents