DROPS

Document

DOI: 10.4230/LIPIcs.CONCUR.2025.30

Open Bisimilarity for the π-Calculus with Mismatch

Authors: Tiange Liu, Alwen Tiu, and Ross Horne

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract

Open bisimilarity is an equivalence relation for the π-calculus that is also congruence, making it suitable to use in compositional reasoning for mobile processes and communication protocols. The original definition of open bisimilarity, due to Sangiorgi, does not account for the mismatch operator, that is crucial in modelling real-world protocols. When mismatch is present, the congruence property no longer holds for open bisimilarity. In a LICS 2018 paper, Horne et al. proposed an extension of open bisimilarity, using a history-indexed class of relations, to address this problem. That definition, however, turns out to be non-compositional as we shall demonstrate in this paper. This paper presents a new definition of open bisimilarity in the π-calculus that incorporates mismatch. This is achieved by augmenting the transition semantics of the π-calculus with an explicit assumption about name distinctions, and by requiring that open bisimulation to be closed under an arbitary extension of the name distinctions assumption. We then prove that the resulting open bisimilarity is both an equivalence relation and a congruence.

Cite as

Tiange Liu, Alwen Tiu, and Ross Horne. Open Bisimilarity for the π-Calculus with Mismatch. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 30:1-30:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{liu_et_al:LIPIcs.CONCUR.2025.30,
  author =	{Liu, Tiange and Tiu, Alwen and Horne, Ross},
  title =	{{Open Bisimilarity for the \pi-Calculus with Mismatch}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{30:1--30:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.30},
  URN =		{urn:nbn:de:0030-drops-239805},
  doi =		{10.4230/LIPIcs.CONCUR.2025.30},
  annote =	{Keywords: mismatch, open bisimilarity, pi calculus}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2023.34

Modal Logics for Mobile Processes Revisited

Authors: Tiange Liu, Alwen Tiu, and Jim de Groot

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract

We revisit the logical characterisations of various bisimilarity relations for the finite fragment of the π-calculus. Our starting point is the early and the late bisimilarity, first defined in the seminal work of Milner, Parrow and Walker, who also proved their characterisations in fragments of a modal logic (which we refer to as the MPW logic). Two important refinements of early and late bisimilarity, called open and quasi-open bisimilarity, respectively, were subsequently proposed by Sangiorgi and Walker. Horne, et. al., showed that open and quasi-bisimilarity are characterised by intuitionistic modal logics: OM (for open bisimilarity) and FM (for quasi-open bisimilarity). In this work, we attempt to unify the logical characterisations of these bisimilarity relations, showing that they can be characterised by different sublogics of a unifying logic. A key insight to this unification derives from a reformulation of the four bisimilarity relations (early, late, open and quasi-open) that uses an explicit name context, and an observation that these relations can be distinguished by the relative scoping of names and their instantiations in the name context. This name context and name substitution then give rise to an accessibility relation in the underlying Kripke semantics of our logic, that is captured logically by an S4-like modal operator. We then show that the MPW, the OM and the FM logics can be embedded into fragments of our unifying classical modal logic. In the case of OM and FM, the embedding uses the fact that intuitionistic implication can be encoded in modal logic S4.

Cite as

Tiange Liu, Alwen Tiu, and Jim de Groot. Modal Logics for Mobile Processes Revisited. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 34:1-34:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{liu_et_al:LIPIcs.CONCUR.2023.34,
  author =	{Liu, Tiange and Tiu, Alwen and de Groot, Jim},
  title =	{{Modal Logics for Mobile Processes Revisited}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{34:1--34:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.34},
  URN =		{urn:nbn:de:0030-drops-190289},
  doi =		{10.4230/LIPIcs.CONCUR.2023.34},
  annote =	{Keywords: pi-calculus, modal logic, intuitionistic logic, bisimilarity}
}

Search Results

Documents authored by Liu, Tiange

Open Bisimilarity for the π-Calculus with Mismatch

Abstract

Cite as

Modal Logics for Mobile Processes Revisited

Abstract

Cite as

Thanks for your feedback!

Could not send message