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Reductions and abstractions for formal verification of distributed round-based algorithms

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Abstract

Model checking has advanced over the last decades to become an effective formal technique for verifying distributed and concurrent systems. As computers grew in memory and processing capacity, it became possible to exhaustively verify systems with billions of states, making it practical to model and verify real-world protocols and algorithms. However, writing a model is a manual task that potentially introduces defects which the model checker tool finds to fulfill the formal specification (e.g., an incorrect model that fulfills an incomplete specification). Furthermore, this kind of formal verification technique is limited by the well-known state-space explosion problem. This paper aims to provide a set of generic template models, appropriate for distributed round-based algorithms, to be used to focus modeling effort on algorithm-specific details. To mitigate state-space explosion, the paper proposes two reduction techniques, named partition symmetry reduction and message order reduction, that exploit symmetries in the state space to avoid expanding equivalent states. The reusable framework for verifying round-based algorithms and the two proposed reduction techniques provide the means for reducing by orders of magnitude the number of states required to analyze common distributed algorithms.

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Acknowledgements

This work is funded by national funds through the FCT - Foundation for Science and Technology, I.P., within the scope of project CISUC - UID/CEC/00326/2020 and by European Social Fund, through the Regional Operational Program Centro 2020, project LASIGE - UIDB/00408/2020, the AESOP project (P2020-31/SI/2017, No. 040004) and through the CMU-Portugal project CAMELOT (POCI-01-0247-FEDER-045915).

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  1. CISUC, Department of Informatics Engineering, University of Coimbra, P-3030 290, Coimbra, Portugal

    Raul Barbosa, Alcides Fonseca & Filipe Araujo

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  1. Raul Barbosa
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  2. Alcides Fonseca
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  3. Filipe Araujo
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Correspondence to Raul Barbosa.

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Barbosa, R., Fonseca, A. & Araujo, F. Reductions and abstractions for formal verification of distributed round-based algorithms. Software Qual J 29, 705–731 (2021). https://doi.org/10.1007/s11219-020-09539-6

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