Skip to main content
SpringerLink
Log in

Quantitative Observables and Averages in Probabilistic Constraint Programming

  • Conference paper
  • First Online:
Book cover New Trends in Constraints (WC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1865))

Included in the following conference series:

Abstract

We investigate notions of observable behaviour of programs which include quantitative aspects of computation along with the most commonly assumed qualitative ones. We model these notions by means of a transition system where transitions occur with a given probability and an associated ‘cost’ expressing some complexity measure (e.g. running time or, in general, resources consumption).

The addition of these quantities allows for a natural formulation of the average behaviour of a program, whose specification and analysis is particularly important in the study of system performance and reliability. It also allows for an average-case analysis of programs’ complexity, which can be seen as a semantical counterpart of the average-case asymptotic analysis of algorithms.

We base our model on the Concurrent Constraint Programming (CCP) paradigm and we argue that it can be an appropriate base for further developments oriented to the analysis and verification of average properties.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Emile Aarts and Jan Korst. Simulated Annealing and Boltzmann Machines. John Wiley & Sons, Chicester, 1989.

    MATH  Google Scholar 

  2. Nicos Angelopoulos, Alessandra di Pierro, and Herbert Wiklicky. Implementing randomised algorithms in constraint logic programming. In JICSLP’98-Joint International Conference and Symposium on Logic Programming, Cambridge, Massachusetts-London, England, 1998. MIT Press.

    Google Scholar 

  3. Marco Bernardo. Theory and Application of Extended Markovian Process Algebra. PhD thesis, University of Bologna, Bologna, February 1999.

    Google Scholar 

  4. Marco Bernardo and Roberto Gorrieri. A tutorial on EMPA: A theory of concurrent processes with nondeterminism, priorities, probabilities and time. Technical Report UBLCS-96-17, Department of Computer Science, University of Bologna, January 1997.

    Google Scholar 

  5. Madhu D.K. Bhabuta. Quantitative Analysis of ATM Networks. PhD thesis, Imperial College, University of London, London, August 1998.

    Google Scholar 

  6. Stefano Bistarelli, Phillipe Codognet, Yan Georget, and Francessca Rossi. Abstracting soft constraint. In K.R. Apt, T. Kakas, E. Monfroy, and F. Rossi, (editors), Proceedings of the ERCIM/COMPULOG Workshop on Constraints, Pahos, Cyprus, 1999.

    Google Scholar 

  7. Stefano Bistarelli, Ugo Montanari, and Francesca Rossi. Semiring-based constraint satisfaction and optimization. Journal of the ACM, 44(2):201–236, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  8. Patrick Cousot and Radhia Cousot. Abstract Interpretation: A Unified Lattice Model for Static Analysis of Programs by Construction or Approximation of Fixpoints. In Proceedings of POPL’77-4th Symposium on Principles of Programming Languages, Los Angeles, CA, pages 238–252, January 1977.

    Google Scholar 

  9. Luca de Alfaro. Formal Verification of Probabilistic Systems. PhD thesis, Stanford University, December 1997.

    Google Scholar 

  10. Luca de Alfaro. How to Specify and Verify the Long-Run Average Behavior of Probabilistic Systems. In Procceedings of LICS’98-13th Symposium on Logic in Computer Science, pages 174–183, Indianapolis, 1998. IEEE Computer Society Press.

    Google Scholar 

  11. Frank S. de Boer, M. Gabbrielli, E. Marchiori, and Catuscia Palamidessi. Proving Concurrent Constraint Programs Correct. ACM Transactions on Programming Languages and Systems, 1997.

    Google Scholar 

  12. Frank S. de Boer and Catuscia Palamidessi. A fully abstract model for concurrent constraint programming. In S. Abramsky and T.S.E. Maibaum, (editors), Proceedings of TAPSOFT/CAAP, volume 493 of Lecture Notes in Computer Science, pages 296–319. Springer-Verlag, 1991.

    Google Scholar 

  13. Alessandra di Pierro and Herbert Wiklicky. An Operational Semantics for Probabilistic Concurrent Constraint Programming. In Y. Choo, P. Iyer and D. Schmidt, (editors), Proceedings of ICCL’ 98-International Conference on Computer Languages, IEEE Computer Society and ACM SIGPLAN, pages 174–183, Chicago, 1998.

    Google Scholar 

  14. Alessandra di Pierro and Herbert Wiklicky. Probabilistic Concurrent Constraint Programming: Towards a fully abstract model. In L. Brim, J. Gruska, and J. Zlatuska, (editors), Proceedings of MFCS’98-Mathematical Foundations of Computer Science, volume 1450 of Lecture Notes in Computer Science, pages 446–455, Berlin-New York, August 1998. Springer Verlag.

    Chapter  Google Scholar 

  15. Alessandra di Pierro and Herbert Wiklicky. Ergodic average in constraint programming. In Marta Kwiatkowska, (editor), Proceedings of PROBMIV’99-2nd International Workshop on Probabilistic Methods in Verification, number CSR-99-8, pages 49–56, Eindhoven, 1999. University of Birmingham.

    Google Scholar 

  16. D. Ferrari. Computer Systems Performance Evaluation. Prentice-Hall, 1978.

    Google Scholar 

  17. Riccardo Focardi. Analysis and Automatic Detection of Information Flows in Systems and Networks. PhD thesis, University of Bologna, Bologna, November 1998.

    Google Scholar 

  18. David E. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading, Massachusetts, 1989.

    MATH  Google Scholar 

  19. Norbert Götz, Ulrich Herzog, and Michael Rettelbach. TIPP — introduction and application to protocol performance analysis. In H. König, (editor), Formale Beschreibungstechniken für verteilte Systeme, FOKUS. Saur Verlag, 1993.

    Google Scholar 

  20. Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley, Reading, Massachusetts, 1989.

    MATH  Google Scholar 

  21. Guido Grandi. Letter to Leibniz (July 1713). In Leibnizens mathematische Schriften, volume 4.

    Google Scholar 

  22. Geoffrey R. Grimmett and D.R. Stirzaker. Probability and Random Processes. Clarendon Press, Oxford, second edition, 1992.

    Google Scholar 

  23. Charles M. Grinstead and J. Laurie Snell. Introduction to Probability American Mathematical Society, Providence, Rhode Island, second revised edition, 1997.

    MATH  Google Scholar 

  24. Vineet Gupta, Radha Jagadeesan, and Vijay A. Saraswat. Probabilistic concurrent constraint programming. In Proceedings of CONCUR’97. Springer Verlag, 1997.

    Google Scholar 

  25. Vintee Gupta, Radha Jagadeesan, and Prakash Panangaden. Stochastic programs as concurrent constraint programs. In Proceedings of POPL’ 99 — 26th Symposium on Principles of Programming Languages, pages 189–202, 1999.

    Google Scholar 

  26. G.W. Hamilton. Usage counting analysis for lazy functional languages. Information and Computation, 146:100–137, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  27. P.G. Harrison and N.M. Patel. Performance Analysis of Communication Networks and Computer Architectures. Addison-Wesley, 1992.

    Google Scholar 

  28. Dorit S. Hochbaum, (editor). Approximation Algorithms for NP-Hard Problems. PWS Publishing Company, Boston, Massachusetts, 1997.

    Google Scholar 

  29. D. E. Knuth. The Art of Computer Programming, Vol.3: Sorting and Searching. Addison-Wesley, 1998. 2nd edition.

    Google Scholar 

  30. Dexter Kozen. Semantics for probabilistic programs. Journal of Computer and System Sciences, 22:328–350, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  31. Patrick D. Lincoln, John C. Mitchell, and Andre Scedrov. Stochastic interaction and Linear Logic. In J.-Y. Girard, Y. Lafont, and L. Regnier, editors, Advances in Linear Logic, volume 222 of London Mathematical Society Lecture Note Series, pages 147–166. Cambridge University Press, Cambridge, 1995.

    Google Scholar 

  32. Rajeev Motwani and Prabhakar Raghavan. Randomized Algorithms. Cambridge University Press, Cambridge, England, 1995.

    MATH  Google Scholar 

  33. Jane Hillstone Marina Ribaud. Stochastic process algebras: A new approach to performance modeling. In K. Bagchi and G. Zobrist, (editors), Modeling and Simulation of Advanced Computer Systems. Gordon Breach, London, 1998.

    Google Scholar 

  34. N. Saheb-Djahromi. CPO’s of measures for nondeterminism. Theoretical Computer Science, 12:19–37, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  35. David Sands. Calculi for Time Analysis of Functional Programs. PhD thesis, Imperial College, University of London, London, September 1990.

    Google Scholar 

  36. Vijay A. Saraswat and Martin Rinard. Concurrent constraint programming. In Proceedings of POPL’ 90-Symposium on Principles of Programming Languages, pages 232–245. ACM, 1990.

    Google Scholar 

  37. Vijay A. Saraswat, Martin Rinard, and Prakash Panangaden. Semantics foundations of concurrent constraint programming. In Proceedings of POPL’ 91-Symposium on Principles of Programming Languages, pages 333–353, 1991.

    Google Scholar 

  38. Roberto Segala. Modelling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, Massachusetts Institute of Technology, June 1995.

    Google Scholar 

  39. Eugene Seneta. Non-negative Matrices and Markov Chains. Springer Verlag, New York-Heidelberg-Berlin, second edition, 1981.

    MATH  Google Scholar 

  40. Henk C. Tijms. Stochastic Models-An Algorithmic Approach. John Wiley & Sons, Chichester, 1994.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Universitá di Pisa, Italy

    Alessandra Di Pierro

  2. Department of Computing, Imperial College, London, UK

    Herbert Wiklicky

Authors
  1. Alessandra Di Pierro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Herbert Wiklicky
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. CWI, Kruislaan 413, 1090, GB Amsterdam, The Netherlands

    Krzysztof R. Apt  & Eric Monfroy  & 

  2. Department of Computer Science, University of Cyprus, 75 Kallipoleos Str., 1678, Nicosia, Cyprus

    Antonis C. Kakas

  3. Department of Pure and Applied Mathematics, University of Padua, Via G. B. Belzoni 7, 35131, Padua, Italy

    Francesca Rossi

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pierro, A.D., Wiklicky, H. (2000). Quantitative Observables and Averages in Probabilistic Constraint Programming. In: Apt, K.R., Monfroy, E., Kakas, A.C., Rossi, F. (eds) New Trends in Constraints. WC 1999. Lecture Notes in Computer Science(), vol 1865. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44654-0_11

Download citation

  • DOI: https://doi.org/10.1007/3-540-44654-0_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67885-4

  • Online ISBN: 978-3-540-44654-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation