On Hierarchical Communication Topologies in the \(\pi \)-calculus

  • Emanuele D’OsualdoEmail author
  • C.-H. Luke Ong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9632)


This paper is concerned with the shape invariants satisfied by the communication topology of \(\pi \text {-term}\)s, and the automatic inference of these invariants. A \(\pi \text {-term}\)P is hierarchical if there is a finite forest \(\mathcal {T}\) such that the communication topology of every term reachable from P satisfies a \(\mathcal {T}\)-shaped invariant. We design a static analysis to prove a term hierarchical by means of a novel type system that enjoys decidable inference. The soundness proof of the type system employs a non-standard view of \(\pi \text {-calculus}\) reactions. The coverability problem for hierarchical terms is decidable. This is proved by showing that every hierarchical term is depth-bounded, an undecidable property known in the literature. We thus obtain an expressive static fragment of the \(\pi \text {-calculus}\) with decidable safety verification problems.


Normal Form Type System Base Type Typing Rule Type Inference 
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.



We would like to thank Damien Zufferey for helpful discussions on the nature of depth boundedness, and Roland Meyer for insightful feedback on a previous version of this paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.TU KaiserslauternKaiserslauternGermany
  2. 2.University of OxfordOxfordUK

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