Comparing Recursion, Replication, and Iteration in Process Calculi

  • Nadia Busi
  • Maurizio Gabbrielli
  • Gianluigi Zavattaro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)


In [BGZ03] we provided a discrimination result between recursive definitions and replication in a fragment of CCS by showing that termination (i.e., all computations terminate) is undecidable in the calculus with recursion, whereas it turns out to be decidable in the calculus with replication. Here we extend the results in [BGZ03] by considering iteration, a third mechanism for expressing infinite behaviours. We show that convergence (i.e., the existence of a terminating computation) is undecidable in the calculus with replication, whereas it is decidable in the calculus with iteration. We also show that recursion, replication and iteration constitute a strict expressiveness hierarchy w.r.t. weak bisimulation: namely, there exist weak bisimulation preserving encodings of iteration in replication (and of replication in recursion), whereas there exist no weak bisimulation preserving encoding in the other direction.


Transition System Transition Rule Program Counter Discrimination Result Random Access Machine 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Nadia Busi
    • 1
  • Maurizio Gabbrielli
    • 1
  • Gianluigi Zavattaro
    • 1
  1. 1.Dipartimento di Scienze dell’InformazioneUniversità di BolognaBolognaItaly

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