Complexity of Checking Bisimilarity between Sequential and Parallel Processes

  • Wojciech Czerwiński
  • Petr Jančar
  • Martin Kot
  • Zdeněk Sawa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8087)


Decidability of bisimilarity for Process Algebra (PA) processes, arising by mixing sequential and parallel composition, is a long-standing open problem. The known results for subclasses contain the decidability of bisimilarity between basic sequential (i.e. BPA) processes and basic parallel processes (BPP). Here we revisit this subcase and derive an exponential-time upper bound. Moreover, we show that the problem if a given basic parallel process is inherently sequential, i.e. bisimilar with an unspecified BPA process, is PSPACE-complete. We also introduce a model of one-counter automata, with no zero tests but with counter resets, that capture the behaviour of processes in the intersection of BPA and BPP.


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  1. 1.
    Benedikt, M., Göller, S., Kiefer, S., Murawski, A.: Bisimilarity of pushdown systems is nonelementary. In: Proc. 28th LiCS. IEEE Computer Society (to appear, 2013)Google Scholar
  2. 2.
    Burkart, O., Caucal, D., Moller, F., Steffen, B.: Verification on infinite structures. In: Handbook of Process Algebra, pp. 545–623. Elsevier (2001)Google Scholar
  3. 3.
    Burkart, O., Caucal, D., Steffen, B.: An elementary decision procedure for arbitrary context-free processes. In: Hájek, P., Wiedermann, J. (eds.) MFCS 1995. LNCS, vol. 969, pp. 423–433. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  4. 4.
    Černá, I., Křetínský, M., Kučera, A.: Comparing expressibility of normed BPA and normed BPP processes. Acta Informatica 36, 233–256 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Czerwinski, W., Fröschle, S.B., Lasota, S.: Partially-commutative context-free processes: Expressibility and tractability. Information and Computation 209(5), 782–798 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Esparza, J.: Petri nets, commutative context-free grammars, and basic parallel processes. Fundamenta Informaticae 31(1), 13–25 (1997)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Hirshfeld, Y., Jerrum, M.: Bisimulation equivalence is decidable for normed process algebra. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 412–421. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    Hirshfeld, Y., Jerrum, M., Moller, F.: A polynomial-time algorithm for deciding bisimulation equivalence of normed basic parallel processes. Mathematical Structures in Computer Science 6, 251–259 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Hirshfeld, Y., Jerrum, M., Moller, F.: A polynomial algorithm for deciding bisimilarity of normed context-free processes. Theor. Comput. Sci. 158, 143–159 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Jančar, P.: Bisimilarity on basic process algebra is in 2-ExpTime (an explicit proof). Logical Methods in Computer Science 9(1) (2013)Google Scholar
  11. 11.
    Jančar, P., Kot, M., Sawa, Z.: Complexity of deciding bisimilarity between normed BPA and normed BPP. Information and Computation 208(10), 1193–1205 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Jančar, P.: Strong bisimilarity on basic parallel processes is PSPACE-complete. In: Proc. 18th LiCS, pp. 218–227. IEEE Computer Society (2003)Google Scholar
  13. 13.
    Jančar, P., Kučera, A., Moller, F.: Deciding bisimilarity between BPA and BPP processes. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 159–173. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Kiefer, S.: BPA bisimilarity is EXPTIME-hard. Information Processing Letters 113(4), 101–106 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Sénizergues, G.: The bisimulation problem for equational graphs of finite out-degree. SIAM J. Comput. 34(5), 1025–1106 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Srba, J.: Strong bisimilarity of simple process algebras: Complexity lower bounds. Acta Informatica 39, 469–499 (2003)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Srba, J.: Roadmap of infinite results. In: Current Trends In Theoretical Computer Science, The Challenge of the New Century, vol. 2, pp. 337–350. World Scientific Publishing Co. (2004), for an updated version see

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Wojciech Czerwiński
    • 1
  • Petr Jančar
    • 2
  • Martin Kot
    • 2
  • Zdeněk Sawa
    • 2
  1. 1.Institute of Computer ScienceUniversity of BayreuthGermany
  2. 2.Dept. of Computer Science, FEITechnical University of OstravaCzech Republic

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