Consensus algorithms are fundamental to the operation of distributed systems, underpinning applications ranging from blockchain technology to distributed databases. However, ensuring the correctness and resilience of these algorithms remains a significant challenge. This paper presents a novel approach to formally verifying consensus algorithms using distributed simulation. We propose a framework that allows for the emulation of a consensus algorithm on a distributed network, facilitating the detection of potential vulnerabilities and failures before deployment. The core of our method involves systematically simulating the algorithm under various failure scenarios, capturing the algorithm's behavior and identifying deviations from expected outcomes. This approach offers a practical and scalable solution for verifying consensus algorithms in real-world distributed systems, contributing to increased system reliability and security. The simulation framework utilizes the following key elements: a model of the consensus algorithm, a distributed network simulator, and a verification engine that analyzes the simulation results. We demonstrate the feasibility and effectiveness of our method through a detailed example, highlighting its potential for broad application in the verification of diverse consensus algorithms.
Distributed consensus algorithms are fundamental to many critical systems, including blockchain networks, sensor networks, and distributed databases. However, these systems are vulnerable to Byzantine faults, where malicious nodes can arbitrarily deviate from the agreed-upon protocol. Verifying the convergence and correctness of consensus algorithms under these conditions is a notoriously difficult problem. This paper presents a novel approach to probabilistic formal verification of distributed consensus algorithms with Byzantine fault tolerance. We model the consensus algorithm as a stochastic process and leverage probability covers and Markov chain analysis to derive rigorous proofs of convergence and fault tolerance. This method allows us to quantify the probability of correct operation even in the presence of arbitrary malicious behavior, offering a significant advancement over traditional approaches that often rely on idealized assumptions. The key contribution lies in the ability to provide probabilistic guarantees for consensus algorithm behavior, rather than simply demonstrating eventual convergence. We illustrate the application of this framework with a simplified example, highlighting its potential for scaling to more complex consensus protocols.
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Distributed systems and fault tolerance
Distributed Control Multi-Agent Systems
Distributed Sensor Networks and Detection Algorithms
This paper presents a novel distributed consensus algorithm designed for commodity networks, specifically focusing on achieving Byzantine fault tolerance. Existing consensus algorithms frequently suffer from complexity and high resource requirements, limiting their applicability in real-world scenarios where network conditions and potential malicious activity are significant concerns. This algorithm addresses these limitations by utilizing the inherent capabilities of commodity networksāsuch as the Internetāto facilitate distributed agreement. A core mechanism is the incorporation of Byzantine fault tolerance techniques, ensuring that the system can maintain agreement even when a fraction of the nodes are compromised and actively attempting to disrupt the consensus process. The proposed algorithm prioritizes simplicity and efficiency, aiming for accessibility on everyday networks while robustly handling potential attacks. The design emphasizes a probabilistic approach to fault detection and recovery, coupled with a novel voting scheme, to achieve both efficiency and resilience. This work aims to broaden the applicability of consensus mechanisms beyond specialized blockchain systems to a wider range of distributed applications.
The emergence of blockchain technologies is changing how we manage data through decentralized, secure systems. In the realm of consensus mechanisms, such as PoW, PoS, and PBFT, several limitations make these technologies inadequate for handling the challenges of IoT-enabled environments and Mutual Distributed Ledgers (MDLs), which require constant and reliable access to their data. These consensus models are reactive, resulting in increased response times (latencies) when a failure or disruption occurs, decreased throughput, and extended recovery periods. The lack of adaptive intelligence to recognize and recover from failures in real-time exacerbates these network failures. This research introduces the Predictive Consensus Algorithm to Blockchain Networks with Failure Detection and Recovery in Real-Time (PCB-FDAR). PCB-FDAR provides a new mechanism by integrating machine learning-based predictive analytics with real-time network monitoring to anticipate future failures and automatically reconfigure the network without human intervention. The framework also enables fault-tolerance across interconnected blockchain environments. PCB-FDAR has been shown through experimentation to outperform traditional consensus mechanisms. When comparing chipsets with an average of 40 blocks, the PCB-FDAR framework achieves an average latency of 1,600 ms, which represents a 42.86% reduction from PoW (2,800 ms) and a 36.00% reduction over PBFT (2,500 ms). In addition, when performing scalability testing, PCBFDAR delivers as high as 1,800 transactions per second (TPS), representing a 450 Ć improvement over PoW (4 TPS) and a 32.7 Ć improvement over PoS (55 TPS). Lastly, the PCBFDAR automatic recovery mechanism reduces failure recovery time from 180 to 30 s, resulting in an 83.33% decrease and providing 99% operational availability. Thus, the results of this study demonstrate that PCB-FDAR provides a scalable, reliable, and fault-tolerant consensus framework for real-time distributed applications.
Abstract Distributed ledgers ā decentralized databases maintained by network consensus ā are often modeled as directed acyclic graphs (DAGs) to capture the causal structure of data addition. Although blockchain systems like Bitcoin use linear chains, alternatives such as tangle in IOTA employ random DAGs. In such mechanisms each new transaction approves multiple predecessors selected through a randomized process. Prior work has established a fluid-limit approximation of the tangleās growth, governed by a delay differential equation. In this paper we go beyond the fluid limit by analyzing the next-order behavior. We show that the fluctuations around the deterministic limit converge to a Gaussian process and derive a stochastic delay differential equation (SDDE) that describes this next-order approximation.
The Genesis Ledger is a computational framework for scalable coordination in complex systems. It demonstrates that stable large-scale organisation cannot be achieved through fixed control alone, but requires three coupled mechanisms: continuous adaptive control, memory of past disturbances, and cross-layer verification of system state. Using a lattice-based model, we show that coordination exhibits a non-linear dependence on coupling strength, with both under-constrained (disordered) and over-constrained (rigid) regimes leading to failure. Adaptive modulation of coupling enables systems to navigate this trade-off, maintaining coherence under dynamic conditions. We further introduce a memory variable that allows the system to reduce recovery time under repeated perturbations, effectively adapting its baseline response to environmental complexity. Finally, we demonstrate that single-layer feedback systems are vulnerable to deceptive or misleading signals, while cross-layer verificationācomparing independent representations of system stateāenables robust filtering of false inputs. Together, these results define a general principle for scalable coordination: Stable systems must continuously regulate constraint, adapt based on experience, and verify signals through consistency across independent representations. This repository provides a reproducible simulation framework, figure generation pipeline, and structured package suitable for further research, validation, and application in distributed systems.
The Genesis Ledger is a computational framework for scalable coordination in complex systems operating under physical constraints. It addresses a fundamental limitation of large-scale coordination: fixed control strategies fail as system size and complexity increase, leading to either incoherence or rigidity-induced collapse. To resolve this, the framework introduces four coupled mechanisms: Adaptive Control: dynamically regulates coupling strength in response to local disorder Memory (Metabolism): reduces recovery time under repeated disturbances through state-dependent adaptation Cross-Layer Verification: ensures consistency between reported system state and underlying physical dynamics, suppressing misleading or deceptive signals Topological Restructuring (Fission): enables systems to maintain coherence at scale by partitioning into smaller units when coordination limits are approached, followed by boundary annealing to prevent instability Using lattice-based simulations, we demonstrate that adaptive systems maintain coherence across regimes where fixed strategies fail. Notably, controlled restructuring does not merely prevent collapse but improves post-transition performance, reframing scaling failure as a reversible process. This work provides: A reproducible simulation framework A figure-generation pipeline for key experimental results A structured architecture for adaptive coordination systems The central result is: Stable coordination at scale is achieved not by increasing control, but by regulating constraint and restructuring before instability becomes irreversible. This framework is applicable to distributed systems, resource allocation networks, and coordination platforms where robustness, scalability, and resistance to adversarial conditions are critical.
This paper addresses the challenge of resilient initial-dependent coordination in multi-agent systems with abnormal nodes. Initial-dependent coordination refers to the process where each node's final value converges to the transformed average of the initial values, with inter-node relationships modeled using augmented transformation matrices. This formulation captures a broad class of coordination and information fusion tasks involving coordinate transformations. We propose a resilient transformed consensus protocol and define the conditions required to achieve initial-dependent coordination in the presence of abnormal nodes. To implement these conditions, we design a distributed accounting and compensation mechanism. Specifically, each node maintains a private ledger that records real-time interaction data with its neighbors. Abnormal behaviors are detected by reconciling accounts with neighboring nodes, leveraging historical interaction information. The accounting mechanism provides a more flexible and effective detection condition. To recover from the impact of abnormal behaviors, we design a distributed compensation scheme that guides normal nodes to adjust their states, mitigating the adverse effects caused by abnormal nodes. Finally, numerical simulations in a sensor network under various abnormal behaviors validate the effectiveness of our approach.
When individual robots have limited sensing capabilities or insufficient fault tolerance, it becomes necessary for multiple robots to form teams during exploration, thereby increasing the collective observation range and reliability. Traditionally, swarm formation has often been managed by a central controller; however, from the perspectives of robustness and flexibility, it is preferable for the swarm to operate autonomously even in the absence of centralized control. In addition, the determination of exploration targets for each team is crucial for efficient exploration in such multi-team exploration scenarios. This study therefore proposes an exploration method that combines (1) an algorithm for self-organization, enabling the autonomous and dynamic formation of multiple teams, and (2) an algorithm that allows each team to autonomously determine its next exploration target (destination). In particular, for (2), this study explores a novel strategy based on large language models (LLMs), while classical frontier-based methods and deep reinforcement learning approaches have been widely studied. The effectiveness of the proposed method was validated through simulations involving tens to hundreds of robots.
Multi-agent coordination and communication models. Multi-agent coordination is reviewed in terms of thearchitectures and algorithms needed to provide autonomous agents with the ability to act as a coordinated force incomplex and dynamic environments. As agentic systems evolve into networks with goals, compelling isolateddecision-making units to become more integrated, structured coordination, and effective communication systems arebecoming increasingly important. This paper compares the available multi-agent coordination models, such ascentralized, decentralized, hierarchical, and swarm-based models, and determines their shortcomings in scalability,latency control, and flexible cooperation. We present a hierarchical classification of organizational strategies ofcoordination and communication protocols specific to the high-autonomy setting, whereby agents are required tonegotiate tasks and settle conflicts as well as exchange contextual information on-the-fly. The paper identifies newproblems in interoperability, trust management, and communication overheads that limit large-scale collaborativeintelligence systems.To solve these shortcomings, the paper presents a new multi-layer collaborative structure combining the perception,reasoning, coordination, and adaptive communication layers with the view of improving the efficiency of the collectivedecision-making. A performance evaluation system is proposed, and it specifies quantifiable indicators like the latencyof coordination, communication overhead, efficiency in task allocation, and the speed of learning adaptation. Thepresented model shows that robustness and scalability can be greatly enhanced by protocol design optimization and adynamic coordination engine in a distributed agent ecosystem, as proposed. This study will help to develop nextgeneration Agentic AI systems that can be trusted to cooperate with other agents and benchmark the competencies andstandards of reliable collaboration in the fields of enterprise automation, finance, robotics, and distributed analytics,thus enhancing the theoretical and practical basis of autonomous collective intelligence.
This article addresses the challenging problem of constrained optimal control for humanāmachine systems subject to external disturbances and the bounded rationality of the human operator. To this end, a novel game-theoretic framework is proposed. Unlike monolithic game formulations, the framework uniquely disaggregates the control problem by transforming it into a multifaceted game via logarithmic barrier functions (BFs): it models humanāmachine cooperation as a positive-sum game oriented toward shared objectives, and disturbance rejection as a zero-sum game tailored for robustness enhancement. To capture the nonideal human decision-making, we integrate the level-$k$reasoning framework to model the operatorās bounded cognitive dynamics. The corresponding coupled HamiltonāJacobiāIsaacs (HJI) equations for this humanāmachine game are derived, and critically, a rigorous proof of global asymptotic stability (GAS) for the transformed system is provided, establishing a solid theoretical foundation. For online implementation without requiring prior knowledge of the system dynamics, we develop a resource-efficient learning architecture based on the adaptive dynamic programming (ADP) and a novel dynamic event-triggered mechanism (DETM). A key feature of this architecture is a fuzzy logic-based module for dynamic authority allocation, which adaptively adjusts control sharing in real time. Rigorous analysis demonstrates that all signals in the closed-loop system are uniformly ultimately bounded and that Zeno behavior is precluded. Simulation results are presented to validate the effectiveness and superiority of the proposed control strategy.
Distributed spectrum allocation for large-scale UAV swarm remains a challenging issue, due to spectrum allocation collisions and the high communication overhead required to reach consensus. To address these challenges, we propose a lightweight consensus protocol for distributed collision-free spectrum allocation (LCCFSA), where UAV nodes in the swarm form a blockchain and spectrum allocation consensus is reached on the chain. Specifically, a fast low-complexity allocation scheme is developed for each UAV based on an interference graph, where each UAV adaptively adjusts its occupancy area to avoid mutual interference. To further reduce the consensus overhead, we design a lightweight consensus protocol with a transaction-based blockchain ledger and provide a formal security analysis of the proposed protocol. A prototype is built to validate the feasibility of the proposed scheme. Simulation results show that the average consensus latency can be reduced by more than 20% in scenarios with 100 consensus nodes.
Distributed ledger technologies rely heavily on consensus mechanisms to maintain a synchronized, tamper-resistant, and decentralized state across a network of mutually untrusted nodes. Conventionally, analyses of these mechanisms concentrate on cryptographic security, equilibrium in game theory, and network latency but often consider system dynamics to be linear predictable or stationary. This paper applies chaos theory to provide an integrated complex systems framework for the nonlinear, dynamic behaviors of three classical blockchain consensus paradigms: Proof of Work (PoW), Proof-of-Stake (PoS), and Byzantine Fault Tolerance (BFT). Through nonlinear feedback loops modeling transaction flows, validator behaviors, and fork-generation processes under the right boundary conditions local computational or stake centralization, sudden network propagation delays, and targeted malicious adversarial perturbations- we prove that deterministic chaos is self-generating. Employing state-space reconstructions, sensitivity analyses to initial conditions, and qualitative descriptions of phase trajectories, this work charts the transition between stable decentralized consensus phases as echoed through chaotic divergence or quasi-permanent chain splits. Results identify major flaws in classical protocols and provide principles to design the next-generation robust chaos-tolerant distributed architectures.
The finite 1-bullet silent duel is considered, involving two duelists who shoot with exponentially-convex accuracy through a uniformly quantized time. The duel is a symmetric matrix game whose optimal value is 0, and each of the duelists has the same optimal behavior, whether it is in pure or mixed strategies. The actual beginning is never optimal in the duel. Apart from the very end of the duel, the conditions for the optimal time moment existence are found. Numerical experiments confirm that the optimality can be manipulated by changing the accuracy factor that scales the payoffs. The results are applicable in systems under limited or censored communication with uncertainty, latency, and lucrative delayed actions. Some examples of such set-ups are time-sensitive information release (privacy and censorship), queueing and load balancing (information science and telecommunication systems), and block proposal timing for decentralized consensus protocols (in Proof-of-Work and Proof-of-Stake).
Ioannis Papastaikoudis, Jeremy D. Watson, Ioannis Lestas
This work explores network coalition-based models using dynamic average consensus protocols, where agents in coalitions interact to reach global agreement. We employ hypergraphs to model communication structures and compare their convergence rates with clique expansion graphs. Our results show that hypergraph-based models achieve faster convergence for the case of continuous consensus dynamical systems and also in discrete time for coalitions with an equal number of agents. Our findings suggest that hypergraphs offer a scalable, decentralized approach to improving consensus algorithms in generalized tree like information structures, with significant potential for enhancing performance in applications like finance and economics.
This paper addresses the design of distributed adaptive control protocols for leader-follower consensus and time-varying formation problems, where agents communicate over directed graphs. Projection operator-based adaptive control protocols are developed for multi-agent systems modelled as general uncertain linear dynamics. An integral sliding mode-based robust control strategy is developed to compensate for the unknown bounded disturbance in the followers' dynamics. To relax the knowledge of the upper bound of the disturbance in designing a sliding-mode controller, a barrier function-based adaptive integral sliding-mode controller is designed to adjust the gain of the discontinuous part of the controller. This technique avoids overestimation of gains, which significantly reduces chattering. This control technique ensures the convergence of disagreement variables in a predefined neighborhood of zero. The Lyapunov-based stability proof demonstrates the convergence of disagreement variables in leader-follower consensus and time-varying formation control problems. Finally, numerical examples are provided to validate the efficacy of the proposed protocols.
Abstract The rise of decentralized technologies introduces challenges in fairness, efficiency, and scalability within distributed ledger protocols. The Internet of Things Applications (IOTA) Tangle, a directed acyclic graph (DAG)-based structure, addresses these challenges by enabling scalable, feeless transactions for IoT applications. This study presents a novel Partially Observable Markov Decision Process (POMDP)-based Tip Selection Algorithm (TSA) to optimize fairness in the IOTA Tangle. The proposed TSA reduces orphaned transactions to as low as 0.003% and eliminates lazy tip selection under medium network loads. Extensive simulations demonstrate that the POMDP-based TSA confirms up to 107 transactions at optimal lambda values, outperforming existing algorithms like Weighted TSA by 328% in efficiency. This algorithm offers significant scalability, fairness, and adaptability, making it a robust solution for IoT-based decentralized applications. These findings advance DAG-based distributed ledger systems by addressing orphaned transactions and lazy behavior, ensuring secure and efficient operations under diverse network conditions.
Unmanned Aerial Vehicles (UAVs) are increasingly deployed in inspection and monitoring missions, yet onboard computation and communication impose significant energy burdens that limit flight time and operational scope. In this work, we introduce a novel, blockchain-enabled framework-grounded in the Distributed Autonomous Organization (DAO) paradigm-for orchestrating distributed analytics across a swarm of UAVs. Leveraging the OASEES project's smart-contract architecture, each drone embeds a Metrics Module for real-time power monitoring, a Behavioral Module for adaptive control, and a Blockchain Agent that autonomously proposes, votes on, and executes collective decisions. Three concurrent threads-Proposal Trigger, Voting, and Action Execution-enable fully decentralized governance of swarm behavior: from detecting critical energy thresholds and formulating swarm-wide conservation maneuvers, to executing approved strategies across all members. We validate our framework in a UAV-based infrastructure inspection scenario, employing a YOLOv5 object-detection pipeline to classify four corrosion classes on a telecommunications mast under three video-capture modalities (short-distance, long-distance, and horizontally concatenated streams). Across all configurations, our system achieves near-perfect precision, recall, and mean Average Precision (mAP50-95$\approx 0.995$), demonstrating both the efficacy of distributed workload inference and the feasibility of treating a single drone as a multi-feed processor. These results underscore the potential of DAO-driven UAV swarms for energy-aware, resilient aerial analytics, and pave the way for fully decentralized 5G/6G-enabled airborne networks.