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The New CAP Theorem on Blockchain Consensus Systems

Author

Listed:
  • Aristidis G. Anagnostakis

    (School of Finance and Administrative Sciences, University of Ioannina Greece, 45110 Ioannina, Greece)

  • Euripidis Glavas

    (School of Informatics and Telecommunications, University of Ioannina Greece, 47100 Arta, Greece)

Abstract

One of the most emblematic theorems in the theory of distributed databases is Eric Brewer’s CAP theorem. It stresses the tradeoffs between Consistency, Availability, and Partition and states that it is impossible to guarantee all three of them simultaneously. Inspired by this, we introduce the new CAP theorem for autonomous consensus systems, and we demonstrate that, at most, two of the three elementary properties, Consensus achievement (C), Autonomy (A), and entropic Performance (P) can be optimized simultaneously in the generic case. This provides a theoretical limit to Blockchain systems’ decentralization, impacting their scalability, security, and real-world adoption. To formalize and analyze this tradeoff, we utilize the IoT micro-Blockchain as a universal, minimal, consensus-enabling framework. We define a set of quantitative functions relating each of the properties to the number of event witnesses in the system. We identify the existing mutual exclusions, and formally prove for one homogenous system consideration, that (A), (C), and (P) cannot be optimized simultaneously. This suggests that a requirement for concurrent optimization of the three properties cannot be satisfied in the generic case and reveals an intrinsic limitation on the design and the optimization of distributed Blockchain consensus mechanisms. Our findings are formally proved utilizing the IoT micro-Blockchain framework and validated through the empirical data benchmarking of large-scale Blockchain systems, i.e., Bitcoin, Ethereum, and Hyperledger Fabric.

Suggested Citation

  • Aristidis G. Anagnostakis & Euripidis Glavas, 2025. "The New CAP Theorem on Blockchain Consensus Systems," Future Internet, MDPI, vol. 17(4), pages 1-24, April.
    • Handle: RePEc:gam:jftint:v:17:y:2025:i:4:p:157-:d:1626363
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    References listed on IDEAS

    as
    1. Sisi Zhou & Kuanching Li & Lijun Xiao & Jiahong Cai & Wei Liang & Arcangelo Castiglione, 2023. "A Systematic Review of Consensus Mechanisms in Blockchain," Mathematics, MDPI, vol. 11(10), pages 1-27, May.
    2. Yaçine Merrad & Mohamed Hadi Habaebi & Elfatih A. A. Elsheikh & Fakher Eldin. M. Suliman & Md Rafiqul Islam & Teddy Surya Gunawan & Mokhtaria Mesri, 2022. "Blockchain: Consensus Algorithm Key Performance Indicators, Trade-Offs, Current Trends, Common Drawbacks, and Novel Solution Proposals," Mathematics, MDPI, vol. 10(15), pages 1-35, August.
    3. Magda Pineda & Daladier Jabba & Wilson Nieto-Bernal & Alfredo Pérez, 2024. "Sustainable Consensus Algorithms Applied to Blockchain: A Systematic Literature Review," Sustainability, MDPI, vol. 16(23), pages 1-26, December.
    4. Andrey L. Bulgakov & Anna V. Aleshina & Sergey D. Smirnov & Alexey D. Demidov & Maxim A. Milyutin & Yanliang Xin, 2024. "Scalability and Security in Blockchain Networks: Evaluation of Sharding Algorithms and Prospects for Decentralized Data Storage," Mathematics, MDPI, vol. 12(23), pages 1-24, December.
    5. Cristian Lepore & Michela Ceria & Andrea Visconti & Udai Pratap Rao & Kaushal Arvindbhai Shah & Luca Zanolini, 2020. "A Survey on Blockchain Consensus with a Performance Comparison of PoW, PoS and Pure PoS," Mathematics, MDPI, vol. 8(10), pages 1-26, October.
    6. Ali Khosravi & Fanni Säämäki, 2023. "Beyond Bitcoin: Evaluating Energy Consumption and Environmental Impact across Cryptocurrency Projects," Energies, MDPI, vol. 16(18), pages 1-23, September.
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