Advertisement

Weak Bisimulation as a Congruence in MSOS

  • Peter D. MossesEmail author
  • Ferdinand Vesely
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9200)

Abstract

MSOS is a variant of structural operational semantics with a natural representation of unobservable transitions. To prove various desirable laws for programming constructs specified in MSOS, bisimulation should disregard unobservable transitions, and it should be a congruence. One approach, following Van Glabbeek, is to add abstraction rules and use strong bisimulation with MSOS specifications in an existing congruence format. Another approach is to use weak bisimulation with specifications in an adaptation of Bloom’s WB Cool congruence format to MSOS. We compare the two approaches, and relate unobservable transitions in MSOS to equations in Rewriting Logic.

Keywords

Label Pattern Label Component Identity Morphism Structural Operational Semantic Readable Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Aceto, L., Fokkink, W., Verhoef, C.: Structural operational semantics. In: Smolka, J.B.P. (ed.) Handbook of Process Algebra, pp. 197–292. Elsevier, Amsterdam (2001)CrossRefGoogle Scholar
  2. 2.
    Bidoit, M., Mosses, P.D.: Casl User Manual - Introduction to Using the Common Algebraic Specification Language. LNCS, vol. 2900. Springer, Heidelberg (2004)zbMATHGoogle Scholar
  3. 3.
    Bloom, B.: Structural operational semantics for weak bisimulations. Theor. Comput. Sci. 146(1–2), 25–68 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bloom, B., Istrail, S., Meyer, A.R.: Bisimulation can’t be traced. J. ACM 42(1), 232–268 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Braga, C.O., Haeusler, E.H., Meseguer, J., Mosses, P.D.: Maude action tool: using reflection to map action semantics to rewriting logic. In: Rus, T. (ed.) AMAST 2000. LNCS, vol. 1816, pp. 407–421. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  6. 6.
    de Braga, C.O., Haeusler, E.H., Meseguer, J., Mosses, P.D.: Mapping modular SOS to rewriting logic. In: Leuschel, M. (ed.) LOPSTR 2002. LNCS, vol. 2664, pp. 262–277. Springer, Heidelberg (2003) CrossRefGoogle Scholar
  7. 7.
    Churchill, M., Mosses, P.D.: Modular bisimulation theory for computations and values. In: Pfenning, F. (ed.) FOSSACS 2013 (ETAPS 2013). LNCS, vol. 7794, pp. 97–112. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  8. 8.
    Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: All About Maude - A High-Performance Logical Framework. LNCS, vol. 4350. Springer, Berlin Heidelberg (2007) zbMATHGoogle Scholar
  9. 9.
    Futatsugi, K., Goguen, J.A., Jouannaud, J.P., Meseguer, J.: Principles of OBJ2. In: POPL 1985, pp. 52–66. ACM, New York (1985)Google Scholar
  10. 10.
    van Glabbeek, R.J.: Bounded nondeterminism and the approximation induction principle in process algebra. Technical report CS-R8634, CWI (1986)Google Scholar
  11. 11.
    van Glabbeek, R.J.: On cool congruence formats for weak bisimulations. Theor. Comput. Sci. 412(28), 3283–3302 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    van Glabbeek, R.J.: Bounded nondeterminism and the approximation induction principle in process algebra. In: Brandenburg, F.J., Vidal-Naquet, G., Wirsing, M. (eds.) STACS 1987. LNCS, vol. 247, pp. 336–347. Springer, Heidelberg (1987) Google Scholar
  13. 13.
    Goguen, J., Kirchner, C., Kirchner, H., Mégrelis, A., Meseguer, J., Winkler, T.: An introduction to OBJ 3. In: Kaplan, S., Jouannaud, J.-P. (eds.) Conditional Term Rewriting Systems. LNCS, vol. 308, pp. 258–263. Springer, Heidelberg (1988) CrossRefGoogle Scholar
  14. 14.
    Goguen, J.A.: Some design principles and theory for OBJ-O, a language to express and execute algebraic specification for programs. In: Blum, E.K., Paul, M., Takasu, S. (eds.) Mathematical Studies of Information Processing. LNCS, vol. 75, pp. 425–473. Springer, Heidelberg (1979) CrossRefGoogle Scholar
  15. 15.
    Goguen, J.A., Jouannaud, J.-P., Meseguer, J.: Operational semantics for order-sorted algebra. In: Brauer, W. (ed.) Automata, Languages and Programming. LNCS, vol. 194, pp. 221–231. Springer, Heidelberg (1985) CrossRefGoogle Scholar
  16. 16.
    Goguen, J.A., Meseguer, J.: Order-sorted algebra solves the constructor-selector, multiple representation and coercion problems. In: LICS 1987, pp. 18–29. IEEE (1987)Google Scholar
  17. 17.
    Goguen, J.A., Meseguer, J.: Order-sorted algebra I: equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theor. Comput. Sci. 105(2), 217–273 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Groote, J.F., Vaandrager, F.: Structured operational semantics and bisimulation as a congruence. Inf. Comput. 100(2), 202–260 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Kirchner, C., Kirchner, H., Meseguer, J.: Operational semantics of OBJ-3. In: Lepistö, T., Salomaa, A. (eds.) Automata, Languages and Programming. LNCS, vol. 317, pp. 287–301. Springer, Heidelberg (1988) CrossRefGoogle Scholar
  20. 20.
    Lamport, L.: The temporal logic of actions. ACM Trans. Program. Lang. Syst. 16(3), 872–923 (1994)CrossRefGoogle Scholar
  21. 21.
    Martí-Oliet, N., Meseguer, J.: Rewriting logic as a logical and semantic framework. Electr. Notes Theor. Comput. Sci. 4, 190–225 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Meseguer, J.: Conditional rewriting logic as a unified model of concurrency. Theor. Comput. Sci. 96(1), 73–155 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Meseguer, J.: Order-sorted parameterization and induction. In: Palsberg, J. (ed.) Semantics and Algebraic Specification. LNCS, vol. 5700, pp. 43–80. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  24. 24.
    Meseguer, J.: Twenty years of rewriting logic. J. Log. Algebr. Program. 81(7–8), 721–781 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Meseguer, J., Goguen, J.A.: Order-sorted algebra solves the constructor-selector, multiple representation, and coercion problems. Inf. Comput. 103(1), 114–158 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Meseguer, J., Roşu, G.: The rewriting logic semantics project: A progress report. Inf. Comput. 231, 38–69 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Milner, R.: Communication and Concurrency. Prentice-Hall Inc., New York (1989)zbMATHGoogle Scholar
  28. 28.
    Milner, R.: Communicating and Mobile Systems: The \(\pi \)-Calculus. Cambridge University Press, New York (1999) zbMATHGoogle Scholar
  29. 29.
    Mosses, P.D.: Foundations of modular SOS. In: Kutyłowski, M., Wierzbicki, T.M., Pacholski, L. (eds.) MFCS 1999. LNCS, vol. 1672, pp. 70–80. Springer, Heidelberg (1999) CrossRefGoogle Scholar
  30. 30.
    Mosses, P.D.: Pragmatics of modular SOS. In: Kirchner, H., Ringeissen, C. (eds.) AMAST 2002. LNCS, vol. 2422, pp. 21–40. Springer, Heidelberg (2002) CrossRefGoogle Scholar
  31. 31.
    Mosses, P.D.: Modular structural operational semantics. J. Log. Algebr. Program. 60–61, 195–228 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Mosses, P.D. (ed.): Casl Reference Manual. LNCS, vol. 2960. Springer, Heidelberg (2004) zbMATHGoogle Scholar
  33. 33.
    Mosses, P.D., Vesely, F.: Weak bisimulation as a congruence in MSOS (extended version). Technical report, PLanCompS (2015). http://www.plancomps.org/wbmsos2015
  34. 34.
    Mousavi, M.R.R., Reniers, M.A.: Congruence for structural congruences. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 47–62. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  35. 35.
    Mousavi, M., Reniers, M.A., Groote, J.F.: SOS formats and meta-theory: 20 years after. Theor. Comput. Sci. 373(3), 238–272 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Plotkin, G.D.: A structural approach to operational semantics. Technical report DAIMI FN-19, University of Aarhus (1981)Google Scholar
  37. 37.
    Plotkin, G.D.: A structural approach to operational semantics. J. Log. Algebr. Program. 60–61, 17–139 (2004)MathSciNetzbMATHGoogle Scholar
  38. 38.
    Sangiorgi, D.: Introduction to Bisimulation and Coinduction. Cambridge University Press, New York (2011) CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Swansea UniversitySwanseaUK

Personalised recommendations