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Genesis and Evolution of ULTraS: Metamodel, Metaequivalences, Metaresults

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Models, Languages, and Tools for Concurrent and Distributed Programming

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11665))

Abstract

We discuss the genesis of the ULTraS metamodel and summarize its evolution arising from the introduction of coherent resolutions of nondeterminism and reachability-consistent semirings.

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Notes

  1. 1.

    Requiring only injectivity as in [3] is not enough because it does not ensure that the former distribution preserves the overall reachability mass of the latter distribution (unlike the probabilistic case, in general there is no predefined reachability mass).

  2. 2.

    The proof is the same as the third property of Proposition 3.5 of [3], which is now correct in its inductive part (\(|\alpha | = n + 1\), \(a' = a\), “either \(\alpha '\) ...”) due to resolution coherency.

  3. 3.

    The definition of \(T_{1} \oplus T_{2}\) before Lemma 4.11 of [3] should be rectified by removing the two instances of “\(\alpha \) occurring only in ...” as resolutions are not coherent there (otherwise the if part of Lemma 4.11(2) would not hold).

References

  1. Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126, 183–235 (1994)

    Article  MathSciNet  Google Scholar 

  2. Bernardo, M.: Non-bisimulation-based Markovian behavioral equivalences. J. Logic Algebraic Program. 72, 3–49 (2007)

    Article  MathSciNet  Google Scholar 

  3. Bernardo, M.: ULTraS at work: compositionality metaresults for bisimulation andtrace semantics. J. Logical Algebraic Methods Program. 94, 150–182 (2018)

    Article  MathSciNet  Google Scholar 

  4. Bernardo, M., De Nicola, R., Loreti, M.: Uniform labeled transition systems for nondeterministic, probabilistic, and stochastic processes. In: Wirsing, M., Hofmann, M., Rauschmayer, A. (eds.) TGC 2010. LNCS, vol. 6084, pp. 35–56. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15640-3_3

    Chapter  Google Scholar 

  5. Bernardo, M., De Nicola, R., Loreti, M.: Uniform labeled transition systems for nondeterministic, probabilistic, and stochastic process calculi. In: Proceedings of the 1st International Workshop on Process Algebra and Coordination, PACO 2011, EPTCS, vol. 60, pp. 66–75 (2011)

    Article  Google Scholar 

  6. Bernardo, M., De Nicola, R., Loreti, M.: A uniform framework for modeling nondeterministic, probabilistic, stochastic, or mixed processes and their behavioral equivalences. Inf. Comput. 225, 29–82 (2013)

    Article  MathSciNet  Google Scholar 

  7. Bernardo, M., De Nicola, R., Loreti, M.: Revisiting trace and testing equivalences for nondeterministic and probabilistic processes. Logical Methods Comput. Sci. 10(1:16), 1–42 (2014)

    MathSciNet  MATH  Google Scholar 

  8. Bernardo, M., De Nicola, R., Loreti, M.: Revisiting bisimilarity and its modal logic for nondeterministic and probabilistic processes. Acta Informatica 52, 61–106 (2015)

    Article  MathSciNet  Google Scholar 

  9. Bernardo, M., Tesei, L.: Encoding timed models as uniform labeled transition systems. In: Balsamo, M.S., Knottenbelt, W.J., Marin, A. (eds.) EPEW 2013. LNCS, vol. 8168, pp. 104–118. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40725-3_9

    Chapter  Google Scholar 

  10. Brookes, S.D., Hoare, C.A.R., Roscoe, A.W.: A theory of communicating sequential processes. J. ACM 31, 560–599 (1984)

    Article  MathSciNet  Google Scholar 

  11. Christoff, I.: Testing equivalences and fully abstract models for probabilistic processes. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 126–138. Springer, Heidelberg (1990). https://doi.org/10.1007/BFb0039056

    Chapter  Google Scholar 

  12. Cleaveland, R., Dayar, Z., Smolka, S.A., Yuen, S.: Testing preorders for probabilistic processes. Inf. Comput. 154, 93–148 (1999)

    Article  MathSciNet  Google Scholar 

  13. De Nicola, R., Hennessy, M.: Testing equivalences for processes. Theor. Comput. Sci. 34, 83–133 (1984)

    Article  MathSciNet  Google Scholar 

  14. De Nicola, R., Latella, D., Loreti, M., Massink, M.: Rate-based transition systems for stochastic process calculi. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 435–446. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02930-1_36

    Chapter  Google Scholar 

  15. De Nicola, R., Latella, D., Loreti, M., Massink, M.: A uniform definition of stochastic process calculi. ACM Comput. Surv. 46(1:5), 1–35 (2013)

    Article  Google Scholar 

  16. Deng, Y., van Glabbeek, R.J., Hennessy, M., Morgan, C.: Characterising testing preorders for finite probabilistic processes. Logical Methods Comput. Sci. 4(4:4), 1–33 (2008)

    MathSciNet  MATH  Google Scholar 

  17. Derman, C.: Finite State Markovian Decision Processes. Academic Press, Cambridge (1970)

    MATH  Google Scholar 

  18. Eisentraut, C., Hermanns, H., Zhang, L.: On probabilistic automata in continuous time. In: Proceedings of the 25th IEEE Symposium on Logic in Computer Science (LICS 2010), pp. 342–351. IEEE-CS Press (2010)

    Google Scholar 

  19. Giacalone, A., Jou, C.-C., Smolka, S.A.: Algebraic reasoning for probabilistic concurrent systems. In: Proceedings of the 1st IFIP Working Conference on Programming Concepts and Methods (PROCOMET 1990), North-Holland, pp. 443–458 (1990)

    Google Scholar 

  20. van Glabbeek, R.J.: The linear time - branching time spectrum I. In: Handbook of Process Algebra, pp. 3–99. Elsevier (2001)

    Google Scholar 

  21. van Glabbeek, R.J., Smolka, S.A., Steffen, B.: Reactive, generative and stratified models of probabilistic processes. Inf. Comput. 121, 59–80 (1995)

    Article  MathSciNet  Google Scholar 

  22. Hansson, H., Jonsson, B.: A calculus for communicating systems with time and probabilities. In: Proceedings of the 11th IEEE Real-Time Systems Symposium (RTSS 1990), pp. 278–287. IEEE-CS Press (1990)

    Google Scholar 

  23. Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. J. ACM 32, 137–162 (1985)

    Article  MathSciNet  Google Scholar 

  24. Hermanns, H., Rettelbach, M.: Syntax, semantics, equivalences, and axioms for MTIPP. In: Proceedings of the 2nd International Workshop on Process Algebra and Performance Modelling (PAPM 1994), pp. 71–87. University of Erlangen, Technical Report 27–4 (1994)

    Google Scholar 

  25. Hillston, J.: A Compositional Approach to Performance Modelling. Cambridge University Press, Cambridge (1996)

    Book  Google Scholar 

  26. Hoare, C.A.R.: Communicating Sequential Processes. Prentice Hall, Upper Saddle River (1985)

    MATH  Google Scholar 

  27. Jonsson, B., Ho-Stuart, C., Yi, W.: Testing and refinement for nondeterministic and probabilistic processes. In: Langmaack, H., de Roever, W.-P., Vytopil, J. (eds.) FTRTFT 1994. LNCS, vol. 863, pp. 418–430. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-58468-4_176

    Chapter  Google Scholar 

  28. Jonsson, B., Yi, W.: Compositional testing preorders for probabilistic processes. In: Proceedings of the 10th IEEE Symposium on Logic in Computer Science (LICS 1995), pp. 431–441. IEEE-CS Press (1995)

    Google Scholar 

  29. Jou, C.-C., Smolka, S.A.: Equivalences, congruences, and complete axiomatizations for probabilistic processes. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 367–383. Springer, Heidelberg (1990). https://doi.org/10.1007/BFb0039071

    Chapter  Google Scholar 

  30. Keller, R.M.: Formal verification of parallel programs. Commun. ACM 19, 371–384 (1976)

    Article  MathSciNet  Google Scholar 

  31. Knast, R.: Continuous-time probabilistic automata. Inf. Control 15, 335–352 (1969)

    Article  MathSciNet  Google Scholar 

  32. Kwiatkowska, M., Norman, G.: A testing equivalence for reactive probabilistic processes. In: Proceedings of the 5th International Workshop on Expressiveness in Concurrency (EXPRESS 1998), ENTCS, vol. 16, no. 2, pp. 114–132. Elsevier (1998)

    Google Scholar 

  33. Kwiatkowska, M., Norman, G., Segala, R., Sproston, J.: Automatic verification of real-time systems with discrete probability distributions. Theor. Comput. Sci. 282, 101–150 (2002)

    Article  MathSciNet  Google Scholar 

  34. Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Inf. Comput. 94, 1–28 (1991)

    Article  MathSciNet  Google Scholar 

  35. Latella, D., Massink, M., de Vink, E.P.: Bisimulation of labelled state-to-function transition systems coalgebraically. Logical Methods Comput. Sci. 11(4:16), 1–40 (2015)

    MathSciNet  MATH  Google Scholar 

  36. Milner, R.: Communication and Concurrency. Prentice Hall, Upper Saddle River (1989)

    MATH  Google Scholar 

  37. Neuhäußer, M.R., Katoen, J.-P.: Bisimulation and logical preservation for continuous-time markov decision processes. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 412–427. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74407-8_28

    Chapter  Google Scholar 

  38. Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981). https://doi.org/10.1007/BFb0017309

    Chapter  Google Scholar 

  39. Parma, A., Segala, R.: Logical characterizations of bisimulations for discrete probabilistic systems. In: Seidl, H. (ed.) FoSSaCS 2007. LNCS, vol. 4423, pp. 287–301. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71389-0_21

    Chapter  MATH  Google Scholar 

  40. Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, Hoboken (1994)

    Book  Google Scholar 

  41. Rabin, M.O.: Probabilistic automata. Inf. Control 6, 230–245 (1963)

    Article  Google Scholar 

  42. Segala, R.: Modeling and verification of randomized distributed real-time systems. PhD thesis (1995)

    Google Scholar 

  43. Segala, R.: A compositional trace-based semantics for probabilistic automata. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 234–248. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-60218-6_17

    Chapter  Google Scholar 

  44. Segala, R.: Testing probabilistic automata. In: Montanari, U., Sassone, V. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 299–314. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61604-7_62

    Chapter  Google Scholar 

  45. Segala, R., Lynch, N.: Probabilistic simulations for probabilistic processes. In: Jonsson, B., Parrow, J. (eds.) CONCUR 1994. LNCS, vol. 836, pp. 481–496. Springer, Heidelberg (1994). https://doi.org/10.1007/978-3-540-48654-1_35

    Chapter  Google Scholar 

  46. Seidel, K.: Probabilistic communicating processes. Theor. Comput. Sci. 152, 219–249 (1995)

    Article  MathSciNet  Google Scholar 

  47. Song, L., Zhang, L., Godskesen, J.C., Nielson, F.: Bisimulations meet PCTL equivalences for probabilistic automata. Logical Methods Comput. Sci. 9(2:7), 1–34 (2013)

    MathSciNet  MATH  Google Scholar 

  48. Stewart, W.J.: Introduction to the Numerical Solution of Markov Chains. Princeton University Press, Princeton (1994)

    MATH  Google Scholar 

  49. Tracol, M., Desharnais, J., Zhioua, A.: Computing distances between probabilistic automata. In: Proceedings of the 9th International Workshop on Quantitative Aspects of Programming Languages (QAPL 2011), EPTCS, vol. 57, pp. 148–162 (2011)

    Article  Google Scholar 

  50. Wolf, V., Baier, C., Majster-Cederbaum, M.: Trace machines for observing continuous-time Markov chains. In: Proceedings of the 3rd International Workshop on Quantitative Aspects of Programming Languages (QAPL 2005), ENTCS, vol. 153, no. 2, pp. 259–277. Elsevier (2005)

    Google Scholar 

  51. Yi, W., Larsen, K.G.: Testing probabilistic and nondeterministic processes. In: Proceedings of the 12th International Symposium on Protocol Specification, Testing and Verification (PSTV 1992), North-Holland, pp. 47–61 (1992)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Scienze Pure e Applicate, Università di Urbino, Urbino, Italy

    Marco Bernardo

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  1. Marco Bernardo
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Editors and Affiliations

  1. Department of Statistics, Computer Science, Applications, University of Florence, Florence, Italy

    Michele Boreale

  2. School of Science and Technology, University of Camerino, Camerino, Italy

    Flavio Corradini

  3. School of Science and Technology, University of Camerino, Camerino, Italy

    Michele Loreti

  4. Department of Statistics, Computer Science, Applications, University of Florence, Florence, Italy

    Rosario Pugliese

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Bernardo, M. (2019). Genesis and Evolution of ULTraS: Metamodel, Metaequivalences, Metaresults. In: Boreale, M., Corradini, F., Loreti, M., Pugliese, R. (eds) Models, Languages, and Tools for Concurrent and Distributed Programming. Lecture Notes in Computer Science(), vol 11665. Springer, Cham. https://doi.org/10.1007/978-3-030-21485-2_7

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