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Accuracy of Message Counting Abstraction in Fault-Tolerant Distributed Algorithms

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10145))

Abstract

Fault-tolerant distributed algorithms are a vital part of mission-critical distributed systems. In principle, automatic verification can be used to ensure the absence of bugs in such algorithms. In practice however, model checking tools will only establish the correctness of distributed algorithms if message passing is encoded efficiently. In this paper, we consider abstractions suitable for many fault-tolerant distributed algorithms that count messages for comparison against thresholds, e.g., the size of a majority of processes. Our experience shows that storing only the numbers of sent and received messages in the global state is more efficient than explicitly modeling message buffers or sets of messages. Storing only the numbers is called message-counting abstraction. Intuitively, this abstraction should maintain all necessary information. In this paper, we confirm this intuition for asynchronous systems by showing that the abstract system is bisimilar to the concrete system. Surprisingly, if there are real-time constraints on message delivery (as assumed in fault-tolerant clock synchronization algorithms), then there exist neither timed bisimulation, nor time-abstracting bisimulation. Still, we prove this abstraction useful for model checking: it preserves ATCTL properties, as the abstract and the concrete models simulate each other.

Supported by: the Austrian Science Fund (FWF) through the National Research Network RiSE (S11403 and S11405), and project PRAVDA (P27722); and by the Vienna Science and Technology Fund (WWTF) through project APALACHE (ICT15-103).

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Notes

  1. 1.

    As we deal with distributed algorithms and timed automata, the notion of a clock appears in two different contexts in this paper, which should not be confused: The problem of clock synchronization is to compute adjustment for the hardware clocks (oscillators). In the context of timed automata, clocks are special variables used to model the timing behavior of a system.

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Authors and Affiliations

  1. TU Wien (Vienna University of Technology), Vienna, Austria

    Igor Konnov & Josef Widder

  2. UnivPM, Ancona, Italy

    Francesco Spegni & Luca Spalazzi

Authors
  1. Igor Konnov
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  2. Josef Widder
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  3. Francesco Spegni
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  4. Luca Spalazzi
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Correspondence to Igor Konnov .

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Editors and Affiliations

  1. IRIF, Université Paris Diderot, Paris, France

    Ahmed Bouajjani

  2. VERIMAG, CNRS & Université Grenoble Alpes, Grenoble, France

    David Monniaux

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Konnov, I., Widder, J., Spegni, F., Spalazzi, L. (2017). Accuracy of Message Counting Abstraction in Fault-Tolerant Distributed Algorithms. In: Bouajjani, A., Monniaux, D. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2017. Lecture Notes in Computer Science(), vol 10145. Springer, Cham. https://doi.org/10.1007/978-3-319-52234-0_19

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  • DOI: https://doi.org/10.1007/978-3-319-52234-0_19

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