Skip to main content

Compositional Methods for Probabilistic Systems

  • Conference paper
  • First Online:
CONCUR 2001 — Concurrency Theory (CONCUR 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2154))

Included in the following conference series:


We present a compositional trace-based model for probabilistic systems. The behavior of a system with probabilistic choice is a stochastic process, namely, a probability distribution on traces, or “bundle.” Consequently, the semantics of a system with both nondeterministic and probabilistic choice is a set of bundles. The bundles of a composite system can be obtained by combining the bundles of the components in a simple mathematical way. Refinement between systems is bundle containment. We achieve assume-guarantee compositionality for bundle semantics by introducing two scoping mechanisms. The first mechanism, which is standard in compositional modeling, distinguishes inputs from outputs and hidden state. The second mechanism, which arises in probabilistic systems, partitions the state into probabilistically independent regions.

This research was supported in part by the SRC contract 99-TJ-683.003, the AFOSR MURI grant F49620-00-1-0327, the MARCO GSRC grant 98-DT-660, the NSF Theory grant CCR-9988172, and the DARPA SEC grant F33615-C-98-3614.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others


  1. R. Alur and T.A. Henzinger. Reactive modules. Formal Methods in System Design 15:7–48, 1999.

    Article  Google Scholar 

  2. M. Abadi and L. Lamport. Conjoining specifications. ACM Trans. Programming Languages and Systems, 17:507–534, 1995.

    Article  Google Scholar 

  3. A. Bianco and L. de Alfaro. Model checking of probabilistic and nondeterministic systems. In Foundations of Software Technology and Theoretical Computer Science, volume 1026 of Lect. Notes in Comp. Sci., pages 499–513. Springer-Verlag, 1995.

    Google Scholar 

  4. L. de Alfaro. Stochastic transition systems. In Concurrency Theory, volume 1466 of Lect. Notes in Comp. Sci., pages 423–438. Springer-Verlag, 1998.

    Google Scholar 

  5. L. de Alfaro, M. Kwiatkowska, G. Norman, D. Parker, and R. Segala. Symbolic model checking of concurrent probabilistic processes using MTBDDs and the Kronecker representation. In Tools and Algorithms for the Construction and Analysis of Systems, volume 1785 of Lect. Notes in Comp. Sci., pages 395–410. Springer-Verlag, 2000.

    Google Scholar 

  6. C. Derman. Finite State Markovian Decision Processes. Academic Press, 1970.

    Google Scholar 

  7. D.L. Dill. Trace Theory for Automatic Hierarchical Verification of Speedindependent Circuits. The MIT Press, 1989.

    Google Scholar 

  8. B. Jonsson and K.G. Larsen. Specification and refinement of probabilistic processes. In Proc. Symp. Logic in Computer Science, pages 266–277. IEEE Computer Society Press, 1991.

    Google Scholar 

  9. L. Lamport. Specifying concurrent program modules. ACM Trans. Progamming Languages and Systems, 5:190–222, 1993.

    Article  Google Scholar 

  10. N.A. Lynch. Distributed Algorithms. Morgan-Kaufmann, 1996.

    Google Scholar 

  11. J. Misra and K.M. Chandy. Proofs of networks of processes. IEEE Trans. Software Engineering, SE-7:417–426, 1981.

    Article  MathSciNet  Google Scholar 

  12. K.L. McMillan. A compositional rule for hardware design refinement. In Computer-Aided Verification, volume 1254 of Lect. Notes in Comp. Sci., pages 24–35. Springer-Verlag, 1997.

    Google Scholar 

  13. R. Segala. Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, MIT, 1995. Technical Report MIT/LCS/TR-676.

    Google Scholar 

  14. R. Segala and N.A. Lynch. Probabilistic simulations for probabilistic processes. In Concurrency Theory, volume 836 of Lect. Notes in Comp. Sci., pages 481–496. Springer-Verlag, 1994.

    Google Scholar 

  15. M.Y. Vardi. Automatic verification of probabilistic concurrent finite-state systems. In Proc. Symp. Foundations of Computer Science, pages 327–338. IEEE Computer Society Press, 1985.

    Google Scholar 

Download references

Author information

Authors and Affiliations


Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

de Alfaro, L., Henzinger, T.A., Jhala, R. (2001). Compositional Methods for Probabilistic Systems. In: Larsen, K.G., Nielsen, M. (eds) CONCUR 2001 — Concurrency Theory. CONCUR 2001. Lecture Notes in Computer Science, vol 2154. Springer, Berlin, Heidelberg.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42497-0

  • Online ISBN: 978-3-540-44685-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics