Formal Verification of Decentralized Consensus Algorithms Using Abstract Interpretation

Abstract

Decentralized consensus algorithms are the foundation of blockchain technology, enabling trustless and secure distributed systems. However, verifying the correctness and security of these algorithms is a formidable challenge due to their inherent complexity, distributed nature, and susceptibility to various failure modes, notably Byzantine faults. This paper proposes a novel approach utilizing abstract interpretation techniques to provide a rigorous and mathematically sound method for formal verification. We leverage techniques like interval analysis and linear arithmetic to construct abstract models of consensus protocols. These models allow us to formally verify crucial properties such as liveness (guaranteeing eventual agreement), safety (preventing incorrect states), and resilience to Byzantine failures. The approach offers a significant advancement over traditional testing and simulation methods, providing a higher degree of confidence in the reliability and security of decentralized consensus algorithms. The core contribution lies in the systematic application of abstract interpretation to model and verify complex, distributed systems, offering a pathway to robust and trustworthy blockchain implementations.