We define the ``Pulse Synchronization'' problem that requires nodes to achieve tight synchronization of regular pulse events, in the settings of distributed computing systems. Pulse-coupled synchronization is a phenomenon displayed by a large variety of biological systems, typically overcoming a high level of noise. Inspired by such biological models, a robust and self-stabilizing Byzantine pulse synchronization algorithm for distributed computer systems is presented. The algorithm attains near optimal synchronization tightness while tolerating up to a third of the nodes exhibiting Byzantine behavior concurrently. Pulse synchronization has been previously shown to be a powerful building block for designing algorithms in this severe fault model. We have previously shown how to stabilize general Byzantine algorithms, using pulse synchronization. To the best of our knowledge there is no other scheme to do this without the use of synchronized pulses.
Clock synchronization is a very fundamental task in distributed system. It thus makes sense to require an underlying clock synchronization mechanism to be highly fault-tolerant. A self-stabilizing algorithm seeks to attain synchronization once lost; a Byzantine algorithm assumes synchronization is never lost and focuses on containing the influence of the permanent presence of faulty nodes. There are efficient self-stabilizing solutions for clock synchronization as well as efficient solutions that are resilient to Byzantine faults. In contrast, to the best of our knowledge there is no practical…
For tolerating Byzantine faults of both the terminal and communication components in self-stabilizing clock synchronization, the two-dimensional self-stabilizing Byzantine-fault-tolerant clock synchronization problem is investigated and solved. By utilizing the time-triggered (TT) stage provided in the underlying networks as TT communication windows, the approximate agreement, hopping procedure, and randomized grandmasters are integrated into the overall solution. It is shown that with partitioning the communication components into $3$ arbitrarily connected subnetworks, efficient synchronizati…
We revisit the approach to Byzantine fault-tolerant clock synchronization based on approximate agreement introduced by Lynch and Welch. Our contribution is threefold: (1) We provide a slightly refined variant of the algorithm yielding improved bounds on the skew that can be achieved and the sustainable frequency offsets. (2) We show how to extend the technique to also synchronize clock rates. This permits less frequent communication without significant loss of precision, provided that clock rates change sufficiently slowly. (3) We present a coupling scheme that allows to make these algorithms …
For reaching dependable high-precision clock synchronization (CS) upon IoT networks, the distributed CS paradigm adopted in ultra-high reliable systems and the master-slave CS paradigm adopted in high-performance but unreliable systems are integrated. Meanwhile, traditional internal clock synchronization is also integrated with external time references to achieve efficient stabilization. Low network connectivity, low complexity, high precision, and high reliability are all considered. To tolerate permanent failures, the Byzantine CS is integrated with the common CS protocols. To tolerate trans…
For reaching fast and efficient self-stabilizing Byzantine pulse synchronization (SSBPS) upon the bounded-delay message-passing networks, we consider the peaceable SSBPS problem where the resource occupation in the stabilized system is required to be as sparse as possible and the stabilization of the system is required to be as fast as possible. To solve it, the decoupled absorption process and emergency process are investigated under a general framework. The constant-time two-stage absorption process and more than one kind of emergency process are provided in integrating the merits of tempora…
The ``Pulse Synchronization'' problem can be loosely described as targeting to invoke a recurring distributed event as simultaneously as possible at the different nodes and with a frequency that is as regular as possible. This target becomes surprisingly subtle and difficult to achieve when facing both transient and permanent failures. In this paper we present an algorithm for pulse synchronization that self-stabilizes while at the same time tolerating a permanent presence of Byzantine faults. The Byzantine nodes might incessantly try to de-synchronize the correct nodes. Transient failures mig…
How to pass from local to global scales in anonymous networks? How to organize a selfstabilizing propagation of information with feedback. From the Angluin impossibility results, we cannot elect a leader in a general anonymous network. Thus, it is impossible to build a rooted spanning tree. Many problems can only be solved by probabilistic methods. In this paper we show how to use Unison to design a self-stabilizing barrier synchronization in an anonymous network. We show that the commuication structure of this barrier synchronization designs a self-stabilizing wave-stream, or pipelining wave,…
We consider the fundamental problem of clock synchronization in a synchronous multi-agent system. Each agent holds a clock with an arbitrary initial value, and clocks must eventually indicate the same value. Previous algorithms worked in static networks with drastic connectivity properties and assumed that global information is available at each agent. In this paper, we propose different solutions for time-varying topologies that require neither strong connectivity nor any global knowledge on the network. First, we study the case of unbounded clocks, and propose a self-stabilizing $MinMax$ alg…
We present a scheme to convert self-stabilizing algorithms that use randomization during and following convergence to self-stabilizing algorithms that use randomization only during convergence. We thus reduce the number of random bits from an infinite number to a bounded number. The scheme is applicable to the cases in which there exits a local predicate for each node, such that global consistency is implied by the union of the local predicates. We demonstrate our scheme over the token circulation algorithm of Herman and the recent constant time Byzantine self-stabilizing clock synchronization…
In extending fast digital clock synchronization to the bounded-delay model, the expected constant time Byzantine pulse resynchronization problem is investigated. In this problem, the synchronized state of the system should not only be deterministically maintained but be reached from arbitrary states with expected constant time in the presence of Byzantine faults. An intuitive geometric representation of the problem is introduced, with which the classical approximate agreement, randomized Byzantine agreement, and random walk are integrated with some geometric operations. Efficient realizations …
Consider an asynchronous network in a shared-memory environment consisting of n nodes. Assume that up to f of the nodes might be Byzantine (n > 12f), where the adversary is full-information and dynamic (sometimes called adaptive). In addition, the non-Byzantine nodes may undergo transient failures. Nodes advance in atomic steps, which consist of reading all registers, performing some calculation and writing to all registers. This paper contains three main contributions. First, the clock-function problem is defined, which is a generalization of the clock synchronization problem. This generaliza…
Byzantine agreement algorithms typically assume implicit initial state consistency and synchronization among the correct nodes and then operate in coordinated rounds of information exchange to reach agreement based on the input values. The implicit initial assumptions enable correct nodes to infer about the progression of the algorithm at other nodes from their local state. This paper considers a more severe fault model than permanent Byzantine failures, one in which the system can in addition be subject to severe transient failures that can temporarily throw the system out of its assumption b…
In this article, we focus on extending the notion of lattice linearity to self-stabilizing programs. Lattice linearity allows a node to execute its actions with old information about the state of other nodes and still preserve correctness. It increases the concurrency of the program execution by eliminating the need for synchronization among its nodes. The extension -- denoted as eventually lattice linear algorithms -- is performed with an example of the service-demand based minimal dominating set (SDDS) problem, which is a generalization of the dominating set problem; it converges in $2n$ mov…
This paper considers the basic $\mathcal{PULL}$ model of communication, in which in each round, each agent extracts information from few randomly chosen agents. We seek to identify the smallest amount of information revealed in each interaction (message size) that nevertheless allows for efficient and robust computations of fundamental information dissemination tasks. We focus on the Majority Bit Dissemination problem that considers a population of $n$ agents, with a designated subset of source agents. Each source agent holds an input bit and each agent holds an output bit. The goal is to let …
We introduce a simple tool called the wavelet (or, r-wavelet) scheme. Wavelets deals with coordination among processes which are at most r hops away of each other. We present a selfstabilizing solution for this scheme. Our solution requires no underlying structure and works in arbritrary anonymous networks, i.e., no process identifier is required. Moreover, our solution works under any (even unfair) daemon. Next, we use the wavelet scheme to design self-stabilizing layer clocks. We show that they provide an efficient device in the design of local coordination problems at distance r, i.e., r-ba…
Robust pulse synchronization is fundamental in constructing reliable synchronous applications in wired and wireless distributed systems. In wired systems, self-stabilizing Byzantine pulse synchronization aims for synchronizing fault-prone distributed components with arbitrary initial states in bounded-delay message-passing systems. In wireless systems, fault-tolerant synchronization of pulse-coupled oscillators is also built for a similar goal but often works under specific system restrictions, such as low computation power, low message complexity, and anonymous physical pulses whose senders c…
Vector clock algorithms are basic wait-free building blocks that facilitate causal ordering of events. As wait-free algorithms, they are guaranteed to complete their operations within a finite number of steps. Stabilizing algorithms allow the system to recover after the occurrence of transient faults, such as soft errors and arbitrary violations of the assumptions according to which the system was designed to behave. We present the first, to the best of our knowledge, stabilizing vector clock algorithm for asynchronous crash-prone message-passing systems that can recover in a wait-free manner …
We present concept and implementation of a self-stabilizing Byzantine fault-tolerant distributed clock generation scheme for multi-synchronous GALS architectures in critical applications. It combines a variant of a recently introduced self-stabilizing algorithm for generating low-frequency, low-accuracy synchronized pulses with a simple non-stabilizing high-frequency, high-accuracy clock synchronization algorithm. We provide thorough correctness proofs and a performance analysis, which use methods from fault-tolerant distributed computing research but also addresses hardware-related issues lik…
Local mutual exclusion guarantees that no two neighboring processes enter a critical section at the same time while satisfying both mutual exclusion and no starvation properties. On the other hand, processes may want to execute some operation simultaneously with the neighbors. Of course, we can use a globally synchronized clock to achieve the task but it is very expensive to realize it in a distributed system in general. In this paper, we define a new concept neighborhood mutual remainder. A distributed algorithm that satisfies the neighborhood mutual remainder requirement should satisfy globa…
We consider the clock synchronization problem in the (discrete) beeping model: Given a network of $n$ nodes with each node having a clock value $δ(v) \in \{0,\ldots T-1\}$, the goal is to synchronize the clock values of all nodes such that they have the same value in any round. As is standard in clock synchronization, we assume \emph{arbitrary activations} for all nodes, i.e., the nodes start their protocol at an arbitrary round (not limited to $\{0,\ldots,T-1\}$). We give an asymptotically optimal algorithm that runs in $4D + \Bigl\lfloor \frac{D}{\lfloor T/4 \rfloor} \Bigr \rfloor \cdot (T \…
Time division multiple access (TDMA) is a method for sharing communication media. In wireless communications, TDMA algorithms often divide the radio time into timeslots of uniform size, $ξ$, and then combine them into frames of uniform size, $τ$. We consider TDMA algorithms that allocate at least one timeslot in every frame to every node. Given a maximal node degree, $δ$, and no access to external references for collision detection, time or position, we consider the problem of collision-free self-stabilizing TDMA algorithms that use constant frame size. We demonstrate that this problem has no …
Phase clocks are synchronization tools that implement a form of logical time in distributed systems. For systems tolerating transient faults by self-repair of damaged data, phase clocks can enable reasoning about the progress of distributed repair procedures. This paper presents a phase clock algorithm suited to the model of transient memory faults in asynchronous systems with read/write registers. The algorithm is self-stabilizing and guarantees accuracy of phase clocks within O(k) time following an initial state that is k-faulty. Composition theorems show how the algorithm can be used for th…
Today's hardware technology presents a new challenge in designing robust systems. Deep submicron VLSI technology introduced transient and permanent faults that were never considered in low-level system designs in the past. Still, robustness of that part of the system is crucial and needs to be guaranteed for any successful product. Distributed systems, on the other hand, have been dealing with similar issues for decades. However, neither the basic abstractions nor the complexity of contemporary fault-tolerant distributed algorithms match the peculiarities of hardware implementations. This pape…
Shared memory emulation can be used as a fault-tolerant and highly available distributed storage solution or as a low-level synchronization primitive. Attiya, Bar-Noy, and Dolev were the first to propose a single-writer, multi-reader linearizable register emulation where the register is replicated to all servers. Recently, Cadambe et al. proposed the Coded Atomic Storage (CAS) algorithm, which uses erasure coding for achieving data redundancy with much lower communication cost than previous algorithmic solutions. Although CAS can tolerate server crashes, it was not designed to recover from une…
