Abstract
Concurrent systems are intrinsically complex and their verification is hampered by the well-known “state-space explosion” issue. Compositional verification is a powerful approach, based on the divide-and-conquer paradigm, to address this issue. Despite impressive results, this approach is not used widely enough in practice, probably because it exists under multiple variants that make knowledge of the field hard to attain. In this article, we highlight the seminal results of Graf & Steffen and propose a survey of compositional verification techniques that exploit (or not) these results.
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Notes
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Some authors consider rendezvous as synchronous and message queues as asynchronous.
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For conciseness, we use the same term “model” and the same letter M to refer both to the “meta-model” (i.e., the low-level formalism) and the “models” (i.e., all particular instances expressed in this formalism).
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Also called subsystems, agents, or processes in the literature.
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In theoretical papers that use M in place of L, there is a notational confusion between \(C_i\) and \([\![C_i]\!]\), which is particularly annoying when the latter cannot be computed.
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Online manuscript at http://www-verimag.imag.fr/~graf/PAPERS/GLS96.pdf.
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Also called context constraints or environment constraints in the literature.
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Also called behavioural interface, interface specifications, or process interface.
- 43.
This operator was actually named reduction in [36], but we prefer the term semi-composition later introduced by Krimm & Mounier [51], because the former term often denotes a minimisation operation that is incompletely done, yielding a smaller yet not necessarily minimal result: partial-order reduction, symmetry reduction, tau-confluence reduction, etc.
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In some cases [36, Sect. 6], interfaces reduce complexity from exponential to linear.
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Such an iterative approach based upon incremental refinement was very much the Cegar idea published ten years later [15].
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Internal actions are usually noted \(\tau \) in most process calculi.
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This state is called cut state in [82].
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A Lotos action can be seen as a value tuple, the first element of which is the gate.
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http://cadp.inria.fr/man/svl-lang.html (see “abstraction”).
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http://cadp.inria.fr/man/svl-lang.html (see “refined abstraction”).
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The present work has been partly funded by Bpi France and Feder (Fonds Européen de Développement Economique Régional) Rhône-Alpes Auvergne under national project SecurIoT-2 supported by the four competitiveness clusters Minalogic, Scs, Systematic Paris-Région, and Derbi.
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Garavel, H., Lang, F., Mounier, L. (2018). Compositional Verification in Action. In: Howar, F., Barnat, J. (eds) Formal Methods for Industrial Critical Systems. FMICS 2018. Lecture Notes in Computer Science(), vol 11119. Springer, Cham. https://doi.org/10.1007/978-3-030-00244-2_13
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