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A Mathematical Model of Parallel Programs and an Approach to Verification of MPI Programs Based on the Proposed Model

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Abstract

This article presents a new mathematical model of parallel programs that can be used, in particular, for verification of parallel programs presented on a certain subset of the MPI parallel programming interface. The model is based on the concepts of sequential and distributed processes. A parallel program is modeled as a distributed process within which sequential processes communicate by asynchronously sending and receiving messages over channels. The main advantage of the proposed model is its capability of modeling and verifying parallel programs that generate an indefinite number of sequential processes. To illustrate the model’s performance, an example of its application to verification of an MPI matrix multiplication program is described.

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Funding

This study was supported by a grant from the Ministry of Digital Development, Communications and Mass Media of the Russian Federation and AO Russian Venture Company (contract no. 004/20 dated March 20, 2020, IGK 0000000007119P190002).

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Authors and Affiliations

  1. Lomonosov Moscow State University, 119991, Moscow, Russia

    A. M. Mironov

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  1. A. M. Mironov
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Correspondence to A. M. Mironov.

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The author declares that he has no conflicts of interest.

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Translated by A. Ovchinnikova

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Mironov, A.M. A Mathematical Model of Parallel Programs and an Approach to Verification of MPI Programs Based on the Proposed Model. Aut. Control Comp. Sci. 56, 762–777 (2022). https://doi.org/10.3103/S014641162207015X

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  • DOI: https://doi.org/10.3103/S014641162207015X

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