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Diamonds for Security: A Non-Interleaving Operational Semantics for the Applied Pi-Calculus

Authors Clément Aubert , Ross Horne , Christian Johansen

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Author Details

Clément Aubert
  • Augusta University, Augusta, GA, USA
Ross Horne
  • University of Luxembourg, Luxembourg
Christian Johansen
  • NTNU - Norwegian University of Science and Technology, Gjøvik, Norway


The authors wish to express their gratitude to the reviewers for their recommendations, that helped us improve our presentation.

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Clément Aubert, Ross Horne, and Christian Johansen. Diamonds for Security: A Non-Interleaving Operational Semantics for the Applied Pi-Calculus. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 30:1-30:26, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


We introduce a non-interleaving structural operational semantics for the applied π-calculus and prove that it satisfies the properties expected of a labelled asynchronous transition system (LATS). LATS have well-studied relations with other standard non-interleaving models, such as Mazurkiewicz traces or event structures, and are a natural extension of labelled transition systems where the independence of transitions is made explicit. We build on a considerable body of literature on located semantics for process algebras and adopt a static view on locations to identify the parallel processes that perform a transition. By lifting, in this way, work on CCS and π-calculus to the applied π-calculus, we lay down a principled foundation for reusing verification techniques such as partial-order reduction and non-interleaving equivalences in the field of security. The key technical device we develop is the notion of located aliases to refer unambiguously to a specific output originating from a specific process. This light mechanism ensures stability, avoiding disjunctive causality problems that parallel extrusion incurs in similar non-interleaving semantics for the π-calculus.

Subject Classification

ACM Subject Classification
  • Theory of computation → Program semantics
  • Theory of computation → Concurrency
  • Theory of computation → Process calculi
  • Security
  • Processes
  • Structural operational semantics
  • Asynchronous transition systems
  • Applied pi-calculus


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