Advertisement

Bisimilarity of Open Terms in Stream GSOS

  • Filippo Bonchi
  • Matias David Lee
  • Jurriaan Rot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10522)

Abstract

Stream GSOS is a specification format for operations and calculi on infinite sequences. The notion of bisimilarity provides a canonical proof technique for equivalence of closed terms in such specifications. In this paper, we focus on open terms, which may contain variables, and which are equivalent whenever they denote the same stream for every possible instantiation of the variables. Our main contribution is to capture equivalence of open terms as bisimilarity on certain Mealy machines, providing a concrete proof technique. Moreover, we introduce an enhancement of this technique, called bisimulation up-to substitutions, and show how to combine it with other up-to techniques to obtain a powerful method for proving equivalence of open terms.

References

  1. 1.
    Aceto, L., Cimini, M., Ingólfsdóttir, A.: Proving the validity of equations in GSOS languages using rule-matching bisimilarity. MSCS 22(2), 291–331 (2012)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Aceto, L., Fokkink, W., Ingolfsdottir, A., Luttik, B.: Finite equational bases in process algebra: results and open questions. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds.) Processes, Terms and Cycles: Steps on the Road to Infinity. LNCS, vol. 3838, pp. 338–367. Springer, Heidelberg (2005). doi: 10.1007/11601548_18 CrossRefGoogle Scholar
  3. 3.
    Baldan, P., Bracciali, A., Bruni, R.: A semantic framework for open processes. Theor. Comput. Sci. 389(3), 446–483 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Bartels, F.: On generalised coinduction and probabilistic specification formats. Ph.D. thesis, CWI, Amsterdam (2004)Google Scholar
  5. 5.
    Bloom, B., Istrail, S., Meyer, A.R.: Bisimulation can’t be traced. J. ACM 42(1), 232–268 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Bonchi, F., Petrisan, D., Pous, D., Rot, J.: A general account of coinduction up-to. Acta Informatica 54(2), 127–190 (2017)Google Scholar
  7. 7.
    de Simone, R.: Higher-level synchronising devices in Meije-SCCS. Theor. Comput. Sci. 37, 245–267 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Hansen, H.H., Klin, B.: Pointwise extensions of GSOS-defined operations. Math. Struct. Comput. Sci. 21(2), 321–361 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Hansen, H.H., Rutten, J.J.M.M.: Symbolic synthesis of mealy machines from arithmetic bitstream functions. Sci. Ann. Comp. Sci. 20, 97–130 (2010)MathSciNetGoogle Scholar
  10. 10.
    Klin, B.: Bialgebras for structural operational semantics: an introduction. Theor. Comput. Sci. 412(38), 5043–5069 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Lucanu, D., Goriac, E.-I., Caltais, G., Roşu, G.: CIRC: a behavioral verification tool based on circular coinduction. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds.) CALCO 2009. LNCS, vol. 5728, pp. 433–442. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-03741-2_30 CrossRefGoogle Scholar
  12. 12.
    Mousavi, M., Reniers, M., Groote, J.: SOS formats and meta-theory: 20 years after. Theor. Comput. Sci. 373(3), 238–272 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Popescu, A., Gunter, E.L.: Incremental pattern-based coinduction for process algebra and its isabelle formalization. In: Ong, L. (ed.) FoSSaCS 2010. LNCS, vol. 6014, pp. 109–127. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-12032-9_9 CrossRefGoogle Scholar
  14. 14.
    Pous, D., Sangiorgi, D.: Enhancements of the bisimulation proof method. In: Advanced Topics in Bisimulation and Coinduction, Cambridge (2012)Google Scholar
  15. 15.
    Rensink, A.: Bisimilarity of open terms. Inf. Comput. 156(1–2), 345–385 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Rutten, J.: Universal coalgebra: a theory of systems. TCS 249(1), 3–80 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Rutten, J.: Elements of stream calculus (an extensive exercise in coinduction). ENTCS 45, 358–423 (2001)zbMATHGoogle Scholar
  18. 18.
    Rutten, J.: A tutorial on coinductive stream calculus and signal flow graphs. TCS 343(3), 443–481 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Turi, D., Plotkin, G.D.: Towards a mathematical operational semantics. In: Proceedings of the LICS 1997, pp. 280–291 (1997)Google Scholar
  20. 20.
    Zantema, H., Endrullis, J.: Proving equality of streams automatically. In: Proceedings of RTA 2011, Novi Sad, Serbia, pp. 393–408 (2011)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2017

Authors and Affiliations

  • Filippo Bonchi
    • 1
  • Matias David Lee
    • 1
  • Jurriaan Rot
    • 2
  1. 1.Univ Lyon, ENS de Lyon, CNRS, UCB Lyon 1, LIPLyonFrance
  2. 2.Radboud UniversityNijmegenThe Netherlands

Personalised recommendations