Skip to main content
Log in

Automated Verification of Multi-Party Agreements and Scheduling of Sending Messages in Distributed Ledger Systems

Programming and Computer Software Aims and scope Submit manuscript


Multi-party agreements are used in distributed ledger systems and blockchain networks to reach an agreement on changes in the system. When one of the network participants proposes a transaction to be recorded, it should be first confirmed by certain network participants. A multi-party agreement or consensus determines who exactly these participants are. Based on the historical data set, one can calculate the transaction confirmation probability for each of the participants. In this work, a method of statistical model checking is proposed to determine the probability that the consensus is reached. Sending confirmation requests may require extra costs. In addition to the stated probability, the mathematical expectation of the number of messages received before reaching a consensus is calculated. A consensus model or several consensus models are given in the form of a Markov chain with various message sending strategies. Based on the construction algorithms for the model and specification, a tool that analyzes consensus and sends confirmation messages is developed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.


  1. Jaoude, J.A. and Saade, R.G., Blockchain applications – usage in different domains, IEEE Access, 2019, vol. 7, pp. 45360–45381.

    Article  Google Scholar 

  2. Bach, L., Branko, M., and Zagar, M., Comparative analysis of blockchain consensus algorithms, MIPRO, 2018, pp. 1545–1550.

    Book  Google Scholar 

  3. Androulaki, E., Barger, A., Bortnikov, V., Cachin, C., Christidis, K., De Caro, A., Enyeart, D., Ferris, C., Laventman, G., and Manevich, Y., Hyperledger fabric: a distributed operating system for permissioned blockchains, EuroSys, 2018, pp. 1–15.

    Book  Google Scholar 

  4. Saad, M., Spaulding, J., Njilla, L., Kamhoua, C., Shetty, S., Nyang, D., and Mohaisen, A., Exploring the attack surface of blockchain: a systematic overview, IEEE, 2020, vol. 22, no. 3, pp. 1977–2008.

  5. Dabholkar, A. and Saraswat, V., Ripping the fabric: attacks and mitigations on hyperledger fabric, Springer, 2019, pp. 300–311.

    Google Scholar 

  6. Baier, C. and Katoen, J., Principles of model checking, MIT press, 2008, pp. 300–311.

    MATH  Google Scholar 

  7. Legay, A., Delahaye, B., and Bensalem, S., Statistical model checking: an overview, Springer, 2010, pp. 122–135.

    Google Scholar 

  8. Fedotov, I.A. and Khritankov, A.S., Systematic review of automatic verification of smart-contracts, Programmnaya Ingeneria, 2020, vol. 11, no. 1, pp. 3–13.

    Article  Google Scholar 

  9. Agha, G. and Palmskog, K., A survey of statistical model checking, ACM Trans, 2018, vol. 28, no. 1, pp. 1–39.

    MathSciNet  Google Scholar 

  10. Fedotov, I. and Khritankov, A., Statistical model checking of common attack scenarios on blockchain, EPTCS, 2021, pp. 65–77.

    Book  Google Scholar 

  11. Imeri, A., Agoulmine, N., and Khadraoui, D., Smart contract modeling and verification techniques: a survey, ADVANCE, 2020, pp. 1–8.

    Google Scholar 

  12. Fedotov I., Khritankov A., and Barger A. Towards automated verification of multi-party consensus protocols, arXiv preprint, 2021.

  13. Zheng, Z., Xie, S., Dai, H., Chen, X., and Wang, H., An overview of blockchain technology: architecture, consensus, and future trends, IEEE, 2017, pp. 557–564.

    Google Scholar 

  14. Cachin, C., Architecture of the hyperledger blockchain fabric, Workshop on distributed cryptocurrencies and consensus ledgers, 2016, vol. 310, no. 4, pp. 1–4.

  15. Duda, J., Exploiting statistical dependencies of time series with hierarchical correlation reconstruction, CoRR, 2018, abs/1807.04119, pp. 11–24.

  16. Corani, G. and Benavoli, A., A bayesian approach for comparing cross-validated algorithms on multiple data sets, Mach. Learn, 2015, vol. 100, no. 2-3, pp. 285–304.

    Article  MathSciNet  MATH  Google Scholar 

  17. Legay, A., Statistical model checking, Springer, 2016, vol. 10000, pp. 478–504.

    MATH  Google Scholar 

  18. Younes, H. and Simmons, R., Probabilistic verification of discrete event systems using acceptance sampling, Springer, 2002, vol. 2404, pp. 223–235.

    Book  MATH  Google Scholar 

  19. Kwiatkowska, M., Norman, G., and Parker, D., PRISM 4.0: verification of probabilistic real-time systems, Springer, 2011, pp. 585–591.

    Google Scholar 

  20. Fedotov, I. and Morounfoluwa, D.O., (accessed February 25, 2022).

  21. Fedotov, I. and Morounfoluwa, D.O., (accessed February 25, 2022).

  22. Gronau Q., Akash Raj N., Wagenmakers E. Informed Bayesian inference for the A/B Test, arXiv preprint, 2019.

Download references

Author information

Authors and Affiliations


Corresponding authors

Correspondence to I. A. Fedotov, A. S. Khritankov or M. D. Obidare.

Additional information

Translated by M. Talacheva

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fedotov, I.A., Khritankov, A.S. & Obidare, M.D. Automated Verification of Multi-Party Agreements and Scheduling of Sending Messages in Distributed Ledger Systems. Program Comput Soft 49, 448–454 (2023).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: