Formal Aspects of Computing

, Volume 24, Issue 4–6, pp 727–748

Probabilistic may/must testing: retaining probabilities by restricted schedulers

Open Access
Original Article

Abstract

This paper considers the probabilistic may/must testing theory for processes having external, internal, and probabilistic choices. We observe that the underlying testing equivalence is too strong and distinguishes between processes that are observationally equivalent. The problem arises from the observation that the classical compose-and-schedule approach yields unrealistic overestimation of the probabilities, a phenomenon that has been recently well studied from the point of view of compositionality, in the context of randomized protocols and in probabilistic model checking. To that end, we propose a new testing theory, aiming at preserving the probability information in a parallel context. The resulting testing equivalence is insensitive to the exact moment the internal and the probabilistic choices occur. We also give an alternative characterization of the testing preorder as a probabilistic ready-trace preorder.

Keywords

Probabilistic may/must testing Restricted schedulers Ready-trace equivalence 

References

  1. ABD11.
    Acciai L, Boreale M, De Nicola R (2011) Linear and may-testing semantics in a probabilistic reactive setting. FMOODS-FORTE’11, LNCS 6722. Springer, Berlin, pp 29–43Google Scholar
  2. Alv10.
    Alvim MS, Andrés ME, Palamidessi C, van Rossum P (2010) Safe equivalences for security properties. IFIP TCS’10, pp 55–70Google Scholar
  3. And11.
    Andrés ME, Palamidessi C, van Rossum P, Sokolova A (2011) Information hiding in probabilistic concurrent systems. Theor Comput Sci 412(28): 3072–3089MATHCrossRefGoogle Scholar
  4. BBK87.
    Baeten JCM, Bergstra JA, Klop JW (1987) Ready-trace semantics for concrete process algebra with the priority operator. Comput J 30(6): 498–506MathSciNetMATHGoogle Scholar
  5. BBR10.
    Baeten JCM, Basten T, Reniers MA (2010) Process algebra: equational theories of communicating processes. Cambridge University PressGoogle Scholar
  6. BiA95.
    Bianco A, de Alfaro L (1995) Model checking of probabilistic and nondeterministic systems. FSTTCS ’95, LNCS 1026. Springer, Berlin, pp 499–513Google Scholar
  7. BHR84.
    Brookes SD, Hoare CAR, Roscoe AW (1984) A theory of communicating sequential processes. J ACM 31(3): 560–599MathSciNetMATHCrossRefGoogle Scholar
  8. Cal10.
    Calin G, Crouzen P, D’Argenio PR, Hahn EM, Zhang L (2010) Time-bounded reachability in distributed input/output interactive probabilistic chains. SPIN’10, LNCS 6349. Springer, Berlin, pp 193–211Google Scholar
  9. Can01.
    Canetti R (2001) Universally composable security: a new paradigm for cryptographic protocols. FOCS’01. IEEE, pp 136–145Google Scholar
  10. Caz03.
    Cazorla D, Cuartero F, Valero V, Pelayo FL, Pardo JJ (2003) Algebraic theory of probabilistic and nondeterministic processes. J Logic Algebraic Programm 55(1–2): 57–103MathSciNetMATHCrossRefGoogle Scholar
  11. ChP07.
    Chatzikokolakis K, Palamidessi C (2007) Making random choices invisible to the scheduler. CONCUR’07, LNCS 4703. Springer, Berlin, pp 42–58Google Scholar
  12. Che06.
    Cheung L, Lynch N, Segala R, Vaandrager F (2006) Switched PIOA: parallel composition via distributed scheduling. Theor Comput Sci 365(1–2): 83–108MathSciNetMATHCrossRefGoogle Scholar
  13. CSV07.
    Cheung L, Stoelinga MIA, Vaandrager FW (2007) A testing scenario for probabilistic processes. J ACM 54(6): 29–12945MathSciNetCrossRefGoogle Scholar
  14. AHJ01.
    de Alfaro L, Henzinger T, Jhala R (2001) Compositional methods for probabilistic systems. In: CONCUR’01, LNCS 2154. Springer, Berlin, pp 351–365Google Scholar
  15. DeH84.
    De Nicola R, Hennessy MCB (1984) Testing equivalences for processes. Theor Comput Sci 34: 83–133MathSciNetMATHCrossRefGoogle Scholar
  16. Den09.
    Deng Y, van Glabbeek R, Hennessy M, Morgan C (2009) Testing finitary probabilistic processes (extended abstract). In: CONCUR’09. LNCS 5710. Springer, Berlin, pp 274–288Google Scholar
  17. Den08.
    Deng Y, van Glabbeek RJ, Hennessy M, Morgan C (2008) Characterising testing preorders for finite probabilistic processes. Logical Methods Comput Sci 4(4): 4–133Google Scholar
  18. Doo53.
    Doob JL (1953) Stochastic processes. Wiley, New YorkMATHGoogle Scholar
  19. DHR08.
    Doyen L, Henzinger TA, Raskin J-F (2008) Equivalence of labeled Markov chains. Int J Found Comput Sci 19(3): 549–563MathSciNetMATHCrossRefGoogle Scholar
  20. Geo11.
    Georgievska S (2011) Probability and hiding in concurrent processes. PhD thesis, Eindhoven University of TechnologyGoogle Scholar
  21. GeA10a.
    Georgievska S, Andova S (2010) Composing systems while preserving probabilities. EPEW 2010, LNCS 6342. Springer, Berlin, pp 268–283Google Scholar
  22. GeA10b.
    Georgievska S, Andova S (2010) Retaining the probabilities in probabilistic testing theory. FOSSACS’10, LNCS 6014. Springer, Berlin, pp 79–93Google Scholar
  23. GeA10c.
    Georgievska S, Andova S (2010) Testing reactive probabilistic processes. QAPL’10, EPTCS 28, pp 99–113Google Scholar
  24. GeA12.
    Georgievska S, Andova S (2012) Probabilistic CSP: preserving the laws via restricted schedulers. MMB & DFT 2012, LNCS 7201. Springer, Berlin, pp 136–150Google Scholar
  25. Gir10.
    Giro S (2010) On the automatic verification of distributed probabilistic automata with partial information. PhD thesis, Universidad Nacional de CórdobaGoogle Scholar
  26. GiD09.
    Giro S, D’Argenio P (2009) On the expressive power of schedulers in distributed probabilistic systems. QAPL’09, ENTCS 253(3). Elsevier, Amsterdam, pp pp 45–71Google Scholar
  27. Gla93.
    van Glabbeek RJ (1993) The linear time-branching time spectrum II. CONCUR’93, LNCS 715. Springer, Berlin, pp 66–81Google Scholar
  28. Gla01.
    van Glabbeek RJ (2001) The linear time-branching time spectrum I; the semantics of concrete, sequential processes. Handbook of process algebra, chap 1. Elsevier, Amsterdam, pp 3–99Google Scholar
  29. GLT09.
    van Glabbeek RJ, Luttik B, Trčka N (2009) Branching bisimilarity with explicit divergence. Fundam Inf 93: 371–392MATHGoogle Scholar
  30. GDR97.
    Gomez FC, De Frutos Escrig D., Ruiz VV (1997) A sound and complete proof system for probabilistic processes. ARTS’97, LNCS 1231. Springer, Berlin, pp 340–352Google Scholar
  31. Han91.
    Hansson HA (1994) Time and probability in formal design of distributed systems. Elsevier, AmsterdamGoogle Scholar
  32. Hen88.
    Hennessy M (1988) Algebraic theory of processes. MIT Press, New YorkMATHGoogle Scholar
  33. Hoa85.
    Hoare CAR (1985) Communicating sequential processes. Prentice Hall, Englewood CliffsMATHGoogle Scholar
  34. How71.
    Howard RA (1971) Semi-Markov and decision processes. Wiley, LondonMATHGoogle Scholar
  35. JoW02.
    Jonsson B, Wang Y (2002) Testing preorders for probabilistic processes can be characterized by simulations. Theor Comput Sci 282(1): 33–51MATHCrossRefGoogle Scholar
  36. KLC98.
    Kaelbling LP, Littman ML, Cassandra AR (1998) Planning and acting in partially observable stochastic domains. Artif Intell J 101: 99–134MathSciNetMATHCrossRefGoogle Scholar
  37. KCS98.
    Kumar KN, Cleaveland R, Smolka SA (1998) Infinite probabilistic and nonprobabilistic testing. FSTTCS’98, LNCS 1530. Springer, Berlin, pp 209–220Google Scholar
  38. KwN98b.
    Kwiatkowska M, Norman G (1998) A testing equivalence for reactive probabilistic processes. EXPRESS’98, ENTCS 16. Elsevier, Amsterdam, pp 1–19Google Scholar
  39. KwN98a.
    Kwiatkowska MZ, Norman GJ (1998) A fully abstract metric-space denotational semantics for reactive probabilistic processes. COMPROX ’98, ENTCS 13. Elsevier, Amsterdam, pp 1–33Google Scholar
  40. LaS91.
    Larsen KG, Skou A (1991) Bisimulation through probabilistic testing. Inf Comput 94: 1–28MathSciNetMATHCrossRefGoogle Scholar
  41. Lid80.
    Lindley DV (1980) Introduction to probability and statistics from a Bayesian viewpoint. Cambridge University Press, CambridgeGoogle Scholar
  42. LNR06.
    López N, Núñez M, Rodríguez I (2006) Specification, testing and implementation relations for symbolic-probabilistic systems. Theor Comput Sci 353(1): 228–248MATHCrossRefGoogle Scholar
  43. Low93.
    Lowe G (1993) Representing nondeterministic and probabilistic behaviour in reactive processes. Technical Report PRG-TR-11-93. Oxford University Computing LabsGoogle Scholar
  44. LSV07.
    Lynch N, Segala R, Vaandrager F (2007) Observing branching structure through probabilistic contexts. SIAM J Comput 37(4): 977–1013MathSciNetMATHCrossRefGoogle Scholar
  45. McM04.
    McIver A, Morgan C (2004) Abstraction, refinement and proof for probabilistic systems (Monographs in Computer Science). Springer, BerlinGoogle Scholar
  46. Mil80.
    Milner R (1980) A calculus of communicating systems. Springer, BerlinMATHCrossRefGoogle Scholar
  47. MMS96.
    Morgan C, McIver A, Seidel K (1996) Probabilistic predicate transformers. ACM Trans Program Lang Syst 18(3): 325–353CrossRefGoogle Scholar
  48. Mor96.
    Morgan C, McIver A, Seidel K, Sanders JW (1996) Refinement-oriented probability for CSP. Formal Aspects Comput 8(6): 617–647MATHCrossRefGoogle Scholar
  49. DeN87.
    De Nicola R (1987) Extensional equivalences for transition systems. Acta Inf 24(2): 211–237MathSciNetMATHGoogle Scholar
  50. PDM07.
    Palmeri MC, De Nicola R, Massink M (2007) Basic observables for probabilistic may testing. QEST ’07. IEEE Computer Society, pp 189–200Google Scholar
  51. Pnu85.
    Pnueli A (1985) Linear and branching structures in the semantics and logics of reactive systems. ICALP’85, LNCS 194. Springer, Berlin, pp 15–32Google Scholar
  52. Put94.
    Puterman ML (1994) Markov decision processes. Wiley, New YorkMATHCrossRefGoogle Scholar
  53. ReV07.
    Rensink A, W Vogler W (2007) Fair testing. Inf Comput 205: 125–198MATHCrossRefGoogle Scholar
  54. Ros98.
    Roscoe AW (1998) The theory and practice of concurrency. Prentice Hall, Englewood CliffsGoogle Scholar
  55. Seg95.
    Segala R (1995) Modeling and verification of randomized distributed real-time systems. PhD thesis, MITGoogle Scholar
  56. Seg96.
    Segala R (1996) Testing probabilistic automata. CONCUR’96, LNCS 1119. Springer, Berlin, pp 299–314Google Scholar
  57. Sei95.
    Seidel K (1995) Probabilistic communicating processes. Theor Comput Sci 152: 219–249MathSciNetMATHCrossRefGoogle Scholar
  58. SMM97.
    Seidel K, Morgan C, McIver A (1997) Probabilistic imperative programming: a rigorous approach. Proceedings of formal methods Pacific ’97. Springer Series in Discrete Mathematics and Theoretical Computer Science, Singapore, Springer, BerlinGoogle Scholar
  59. Sod71.
    Sondik EJ (1971) The optimal control of partially observable Markov processes. PhD thesis, Stanford UniversityGoogle Scholar
  60. WaL92.
    Wang Y, Larsen KG (1992) Testing probabilistic and nondeterministic processes. Proceedings of IFIP TC6/WG6.1 twelth international symposium on protocol specification, testing and verification XII, pp 47–61Google Scholar
  61. WSS97.
    Wu S-H, Smolka SA, Stark E (1997) Composition and behaviors of probabilistic I/O automata. Theor Comput Sci 176(1–2): 1–38MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands

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