3 Search Results for "Johansen, Christian"

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Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2024.157

Domain Reasoning in TopKAT

Authors: Cheng Zhang, Arthur Azevedo de Amorim, and Marco Gaboardi

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

TopKAT is the algebraic theory of Kleene algebra with tests (KAT) extended with a top element. Compared to KAT, one pleasant feature of TopKAT is that, in relational models, the top element allows us to express the domain and codomain of a relation. This enables several applications in program logics, such as proving under-approximate specifications or reachability properties of imperative programs. However, while TopKAT inherits many pleasant features of KATs, such as having a decidable equational theory, it is incomplete with respect to relational models. In other words, there are properties that hold true of all relational TopKATs but cannot be proved with the axioms of TopKAT. This issue is potentially worrisome for program-logic applications, in which relational models play a key role. In this paper, we further investigate the completeness properties of TopKAT with respect to relational models. We show that TopKAT is complete with respect to (co)domain comparison of KAT terms, but incomplete when comparing the (co)domain of arbitrary TopKAT terms. Since the encoding of under-approximate specifications in TopKAT hinges on this type of formula, the aforementioned incompleteness results have a limited impact when using TopKAT to reason about such specifications.

Cite as

Cheng Zhang, Arthur Azevedo de Amorim, and Marco Gaboardi. Domain Reasoning in TopKAT. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 157:1-157:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{zhang_et_al:LIPIcs.ICALP.2024.157,
  author =	{Zhang, Cheng and de Amorim, Arthur Azevedo and Gaboardi, Marco},
  title =	{{Domain Reasoning in TopKAT}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{157:1--157:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.157},
  URN =		{urn:nbn:de:0030-drops-203003},
  doi =		{10.4230/LIPIcs.ICALP.2024.157},
  annote =	{Keywords: Kleene algebra, Kleene Algebra With Tests, Kleene Algebra With Domain, Kleene Algebra With Top and Tests, Completeness, Decidability}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2022.29

A Kleene Theorem for Higher-Dimensional Automata

Authors: Uli Fahrenberg, Christian Johansen, Georg Struth, and Krzysztof Ziemiański

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

Abstract

We prove a Kleene theorem for higher-dimensional automata (HDAs). It states that the languages they recognise are precisely the rational subsumption-closed sets of interval pomsets. The rational operations include a gluing composition, for which we equip pomsets with interfaces. For our proof, we introduce HDAs with interfaces as presheaves over labelled precube categories and use tools inspired by algebraic topology, such as cylinders and (co)fibrations. HDAs are a general model of non-interleaving concurrency, which subsumes many other models in this field. Interval orders are used as models for concurrent or distributed systems where events extend in time. Our tools and techniques may therefore yield templates for Kleene theorems in various models and applications.

Cite as

Uli Fahrenberg, Christian Johansen, Georg Struth, and Krzysztof Ziemiański. A Kleene Theorem for Higher-Dimensional Automata. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fahrenberg_et_al:LIPIcs.CONCUR.2022.29,
  author =	{Fahrenberg, Uli and Johansen, Christian and Struth, Georg and Ziemia\'{n}ski, Krzysztof},
  title =	{{A Kleene Theorem for Higher-Dimensional Automata}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.29},
  URN =		{urn:nbn:de:0030-drops-170925},
  doi =		{10.4230/LIPIcs.CONCUR.2022.29},
  annote =	{Keywords: higher-dimensional automata, interval posets, Kleene theorem, concurrency theory, labelled precube categories}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2022.30

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

Authors: Clément Aubert, Ross Horne, and Christian Johansen

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

Abstract

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.

Cite as

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)

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@InProceedings{aubert_et_al:LIPIcs.CONCUR.2022.30,
  author =	{Aubert, Cl\'{e}ment and Horne, Ross and Johansen, Christian},
  title =	{{Diamonds for Security: A Non-Interleaving Operational Semantics for the Applied Pi-Calculus}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{30:1--30:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.30},
  URN =		{urn:nbn:de:0030-drops-170930},
  doi =		{10.4230/LIPIcs.CONCUR.2022.30},
  annote =	{Keywords: Security, Processes, Structural operational semantics, Asynchronous transition systems, Applied pi-calculus}
}

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2 Johansen, Christian
1 Aubert, Clément
1 Fahrenberg, Uli
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1 Theory of computation → Automata extensions
1 Theory of computation → Concurrency
1 Theory of computation → Formal languages and automata theory
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1 Applied pi-calculus
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