License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2023.137
URN: urn:nbn:de:0030-drops-181895
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18189/
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Vaandrager, Frits ; Wißmann, Thorsten

Action Codes

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LIPIcs-ICALP-2023-137.pdf (0.9 MB)

Abstract

We provide a new perspective on the problem how high-level state machine models with abstract actions can be related to low-level models in which these actions are refined by sequences of concrete actions. We describe the connection between high-level and low-level actions using action codes, a variation of the prefix codes known from coding theory. For each action code ℛ, we introduce a contraction operator α_ℛ that turns a low-level model ℳ into a high-level model, and a refinement operator ϱ_ℛ that transforms a high-level model ? into a low-level model. We establish a Galois connection ϱ_ℛ(?) ⊑ ℳ ⇔ ? ⊑ α_ℛ(ℳ), where ⊑ is the well-known simulation preorder. For conformance, we typically want to obtain an overapproximation of model ℳ. To this end, we also introduce a concretization operator γ_ℛ, which behaves like the refinement operator but adds arbitrary behavior at intermediate points, giving us a second Galois connection α_ℛ(ℳ) ⊑ ? ⇔ ℳ ⊑ γ_ℛ(?). Action codes may be used to construct adaptors that translate between concrete and abstract actions during learning and testing of Mealy machines. If Mealy machine ℳ models a black-box system then α_ℛ(ℳ) describes the behavior that can be observed by a learner/tester that interacts with this system via an adaptor derived from code ℛ. Whenever α_ℛ(ℳ) implements (or conforms to) ?, we may conclude that ℳ implements (or conforms to) γ_ℛ (?).
Almost all results, examples, and counter-examples are formalized in Coq.

BibTeX - Entry

@InProceedings{vaandrager_et_al:LIPIcs.ICALP.2023.137,
  author =	{Vaandrager, Frits and Wi{\ss}mann, Thorsten},
  title =	{{Action Codes}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{137:1--137:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18189},
  URN =		{urn:nbn:de:0030-drops-181895},
  doi =		{10.4230/LIPIcs.ICALP.2023.137},
  annote =	{Keywords: Automata, Models of Reactive Systems, LTS, Action Codes, Action Refinement, Action Contraction, Galois Connection, Model-Based Testing, Model Learning}
}

Keywords: Automata, Models of Reactive Systems, LTS, Action Codes, Action Refinement, Action Contraction, Galois Connection, Model-Based Testing, Model Learning
Collection: 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Issue Date: 2023
Date of publication: 05.07.2023
Supplementary Material: Software: https://gitlab.science.ru.nl/twissmann/action-codes-coq archived at: https://archive.softwareheritage.org/swh:1:dir:953b24c1e0771ce9ed7961f59f07294e0fd615d2

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