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.
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.
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).
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.
The proliferation of unmanned aerial vehicle (UAV) swarms in mission-critical applications for 6G and the Internet of Things (IoT) introduces significant security vulnerabilities stemming from their dynamic, distributed, and resource-constrained nature. Traditional security paradigms are often inadequate for these complex cyber-physical systems. This paper proposes a novel, cross-layer security framework that ensures robust and lightweight operation for UAV swarms. The framework is founded on a novel Entropy-Derived Physically Unclonable Function (EPUF) based on DRAM, which employs a data-driven characterization process designed to achieve near 100% reliability in simulation through a data-driven characterization process, which is validated through extensive simulation, addressing a critical limitation of conventional PUFs. To counteract sophisticated threats, we formulate the key management problem as a Markov Decision Process (MDP) and introduce a deep reinforcement learning (DRL) agent that dynamically optimizes key update frequency, balancing security posture against energy consumption. Furthermore, we leverage a lightweight, permissioned blockchain as a decentralized trust anchor for public key management, providing an immutable and resilient ledger and enhancing the principles of distributed and edge intelligence. The core authentication protocol's security is formally verified using the ProVerif tool and Belief Logic, proving its robustness against a Dolev-Yao adversary. Experimental simulations demonstrate that our framework significantly outperforms conventional methods, reducing authentication latency and energy consumption by over 95% compared to PKI-based schemes while effectively mitigating replay and impersonation attacks.
Navigation in unstructured, GPS-denied environments, such as forests and agricultural fields, poses persistent challenges for heterogeneous robotic teams. While visual homing and Wide Area Visual Navigation (WAVN) enable lightweight, map-free operation, their effectiveness in large-scale, decentralized settings can be constrained by the absence of a coordination mechanism that accounts for varying reliability across robots. This article examines the innovative combination of blockchain techniques with WAVN to tackle visual navigation issues in diverse mobile robots used in unstructured sectors like agriculture and forestry. It addresses GPS reliance, adapts to environmental shifts, and reduces computational burdens by integrating RoboStake, a novel blockchain Proof-of-Stake (PoS) mechanism, into the WAVN system. This solution seeks to bolster cooperative navigation by assessing the reliability of each robotās navigational input. With methods including a stake weight function, a PoS consensus score, and a navigability function, this strategy confronts the computational hurdles of coordinating robots and verifying data. Lastly, we showcase how the proposed approach upholds critical navigability features of the WAVN system and present results from scalable simulation experiments to highlight the improved efficiency achieved through enhanced cooperation.
This work develops a novel two-phase control framework that enables a swarm of compact spacecraft (agents), such as CubeSats and Nanosats, to autonomously capture tumbling and uncooperative targets. By leveraging decentralized, bio-inspired swarm behavior control and distributed coordination strategies, the proposed system enables fully interchangeable agents to achieve robust, leaderless self-organization. During the capture, flocking behavior guides agents towards the target, while anti-flocking behavior enforces uniform dispersion of agents around it to provide full surface coverage and effective encapsulation prior to capture. A consensus-based protocol synchronizes the capture action among agents by allowing all agents to agree on a common action time. In this process, each agent autonomously identifies available capture points and participates in an auction-based allocation algorithm to collectively allocate optimal capture positions among agents. Simulation results validate the effectiveness of the proposed framework in autonomously capturing targets of various shapes, sizes and motion patterns, and demonstrate scalability across different swarm sizes. Overall, the proposed approach shows significant potential for coordinated, efficient, and robust swarm-based capture of uncooperative targets in space, offering benefits in scalability, adaptability, robustness, and cost-effectiveness.
Robotic swarm intelligence is a rapidly evolving field that leverages principles of decentralized control, self-organization, and emergent behavior to enable effective coordination and collaboration in multi-robot systems. Inspired by biological swarms, such as ant colonies and bird flocks, swarm robotics focuses on the collective performance of simple agents interacting locally to achieve complex tasks. This approach enhances scalability, robustness, and adaptability in dynamic and unpredictable environments. Key applications include search and rescue, environmental monitoring, industrial automation, and military operations. Recent advancements in artificial intelligence, machine learning, and communication technologies have further improved swarm decision-making, task allocation, and formation control. This paper explores the fundamental principles, coordination strategies, and challenges in robotic swarm intelligence, highlighting future directions for optimizing collaboration in autonomous multi-robot systems.
This paper introduces a novel architecture for a distributed ledger, commonly referred to as a "blockchain", which is organized in the form of directed acyclic graph (DAG) with UTXO transactions as vertices, rather than as a chain of blocks. Consensus on the state of ledger assets is achieved through the cooperative consensus: an profit-driven behavior of token holders themselves, which is viable only when they cooperate by following the "biggest ledger coverage rule", akin the "longest chain rule" of Bitcoin. The cooperative behavior is facilitated by enforcing purposefully designed UTXO transaction validity constraints. Token holders are the sole category of participants authorized to make amendments to the ledger, making participation completely permissionless - without miners, validators, committees or staking - and without any need of knowledge about the composition of the set of all participants in the consensus. The setup allows to achieve high throughput and scalability alongside with low transaction costs, while preserving key aspects of high decentralization, open participation, and asynchronicity found in Bitcoin and other proof-of-work blockchains, but without huge energy consumption. Sybil protection is achieved similarly to proof-of-stake blockchains, using tokens native to the ledger, yet the architecture operates in a leaderless manner without block proposers and committee selection.
Unmanned Aerial Vehicles (UAVs) are pivotal in enhancing connectivity in diverse applications such as search and rescue, remote communications, and battlefield networking, especially in environments lacking ground-based infrastructure. This paper introduces a novel approach that harnesses Multi-Agent Deep Reinforcement Learning to optimize UAV communication systems. The methodology, centered on the Independent Proximal Policy Optimization technique, significantly improves fairness, throughput, and energy efficiency by enabling UAVs to autonomously adapt their operational strategies based on real-time environmental data and individual performance metrics. Moreover, the integration of Distributed Ledger Technologies with Multi-Agent Deep Reinforcement Learning enhances the security and scalability of UAV communications, ensuring robustness against disruptions and adversarial attacks. Extensive simulations demonstrate that this approach surpasses existing benchmarks in critical performance metrics, highlighting its potential implications for future UAV-assisted communication networks. By focusing on these technological advancements, the groundwork is laid for more efficient, fair, and resilient UAV systems.
Ayush M. Patil, Atharv S. Pakmode, Rishi Jain, Rupali D. Rode Ā· 5 authors
Swarm robotics is a broad area of study that looks at the collective behavior of many autonomous robots to complete challenging tasks. Swarm robotics attempts to take advantage of the power of decentralization and self-organization to achieve adaptability, scalability, and robustness in robotic systems by taking inspiration from the collective behavior of natural swarms, such as ants, bees, and schools of fish.
With the continuous development of UAV technology, the application of UAV swarm in the military field is gradually becoming the focus of research around the world. Although it can bring a series of benefits in autonomous cooperation, the traditional UAV management technology is prone to hacker attacks due to many security issues such as a single point of failure brought by centralized management. Because of the advantages of distributed, tamper-proof, and traceability, blockchain is applied to UAV swarm to solve some of the security problems caused by centralized management. However, due to the limitations of its consensus algorithm Practical Byzantine Fault Tolerance (PBFT), its communication complexity will increase rapidly with the increase of the number of nodes, which also leads to the poor scalability of the algorithm and can only be applied to small-scale networks. To use the PBFT algorithm in large-scale networks such as UAV swarm, a dynamic and highly trusted PBFT (DTPBFT) algorithm is proposed in this paper. Firstly, a new consensus algorithm model including consensus layer and verification layer is designed. Then, a consensus node election scheme based on trust mechanism is proposed under this model. The trust degree of nodes in the blockchain network is comprehensively evaluated by selecting several representative indicators, and the weight factor of each indicator is calculated by entropy weight method. It not only reduces the communication complexity, but also ensures the reliability and dynamic update of consensus nodes. Experiments show that when the number of UAVs is 200, the consensus time of DTPBFT is 0.24 s, which indicates that this algorithm can support large-scale UAV swarm without causing communication congestion, so it has good scalability. In addition, experiments also show that DTPBFT can tolerate more than 13 malicious nodes, which improves the fault tolerance rate of PBFT.