arXiv subjects

Ulrich Schmid

Publications and source records attributed to Ulrich Schmid.

49 records · Page 3Linked to original sources

arXiv2017

Consensus in Rooted Dynamic Networks with Short-Lived Stability

We consider the problem of solving consensus using deterministic algorithms in a synchronous dynamic network with unreliable, directional point-to-point links, which are under the control of a message adversary. In contrast to a large body of existing work that focuses on oblivious message adversaries where the communication graphs are picked from a predefined set, we consider message adversaries where guarantees about stable periods that occur only eventually can be expressed. We reveal to what extent such eventual stability is necessary and sufficient, that is, we present the shortest period of stability that permits solving consensus, a result that should prove quite useful in systems that exhibit erratic boot-up phases or recover after repeatedly occurring, massive transient faults. Contrary to the case of longer stability periods, where we show how standard algorithmic techniques for solving consensus can be employed, the short-lived nature of the stability phase forces us to use more unusual algorithmic methods that avoid waiting explicitly for the stability period to occur.

cs.DC↗

arXiv2015

Fast Consensus under Eventually Stabilizing Message Adversaries

This paper is devoted to deterministic consensus in synchronous dynamic networks with unidirectional links, which are under the control of an omniscient message adversary. Motivated by unpredictable node/system initialization times and long-lasting periods of massive transient faults, we consider message adversaries that guarantee periods of less erratic message loss only eventually: We present a tight bound of $2D+1$ for the termination time of consensus under a message adversary that eventually guarantees a single vertex-stable root component with dynamic network diameter $D$, as well as a simple algorithm that matches this bound. It effectively halves the termination time $4D+1$ achieved by an existing consensus algorithm, which also works under our message adversary. We also introduce a generalized, considerably stronger variant of our message adversary, and show that our new algorithm, unlike the existing one, still works correctly under it.

cs.DC↗

arXiv2015

Gracefully Degrading Consensus and $k$-Set Agreement in Directed Dynamic Networks

We study distributed agreement in synchronous directed dynamic networks, where an omniscient message adversary controls the availability of communication links. We prove that consensus is impossible under a message adversary that guarantees weak connectivity only, and introduce vertex-stable root components (VSRCs) as a means for circumventing this impossibility: A VSRC(k, d) message adversary guarantees that, eventually, there is an interval of $d$ consecutive rounds where every communication graph contains at most $k$ strongly (dynamic) connected components consisting of the same processes, which have at most outgoing links to the remaining processes. We present a consensus algorithm that works correctly under a VSRC(1, 4H + 2) message adversary, where $H$ is the dynamic causal network diameter. On the other hand, we show that consensus is impossible against a VSRC(1, H - 1) or a VSRC(2, $\infty$) message adversary, revealing that there is not much hope to deal with stronger message adversaries. However, we show that gracefully degrading consensus, which degrades to general $k$-set agreement in case of unfavourable network conditions, is feasible against stronger message adversaries: We provide a $k$-uniform $k$-set agreement algorithm, where the number of system-wide decision values $k$ is not encoded in the algorithm, but rather determined by the actual power of the message adversary in a run: Our algorithm guarantees at most $k$ decision values under a VSRC(n, d) + MAJINF(k) message adversary, which combines VSRC(n, d) (for some small $d$, ensuring termination) with some information flow guarantee MAJINF(k) between certain VSRCs (ensuring $k$-agreement). Our results provide a significant step towards the exact solvability/impossibility border of general $k$-set agreement in directed dynamic networks.

cs.DC↗

arXiv2014

A Framework for Automated Competitive Analysis of On-line Scheduling of Firm-Deadline Tasks

We present a flexible framework for the automated competitive analysis of on-line scheduling algorithms for firm-deadline real-time tasks based on multi-objective graphs: Given a taskset and an on-line scheduling algorithm specified as a labeled transition system, along with some optional safety, liveness, and/or limit-average constraints for the adversary, we automatically compute the competitive ratio of the algorithm w.r.t. a clairvoyant scheduler. We demonstrate the flexibility and power of our approach by comparing the competitive ratio of several on-line algorithms, including $D^{over}$, that have been proposed in the past, for various tasksets. Our experimental results reveal that none of these algorithms is universally optimal, in the sense that there are tasksets where other schedulers provide better performance. Our framework is hence a very useful design tool for selecting optimal algorithms for a given application.

cs.DS↗

arXiv2014

Faithful Glitch Propagation in Binary Circuit Models

Modern digital circuit design relies on fast digital timing simulation tools and, hence, on accurate binary-valued circuit models that faithfully model signal propagation, even throughout a complex design. Unfortunately, it was recently proved [Függer et al., ASYNC'13] that no existing binary-valued circuit model proposed so far, including the two most commonly used pure and inertial delay channels, faithfully captures glitch propagation: For the simple Short-Pulse Filtration (SPF) problem, which is related to a circuit's ability to suppress a single glitch, we showed that the quite broad class of bounded single-history channels either contradict the unsolvability of SPF in bounded time or the solvability of SPF in unbounded time in physical circuits. In this paper, we propose a class of binary circuit models that do not suffer from this deficiency: Like bounded single-history channels, our involution channels involve delays that may depend on the time of the previous output transition. Their characteristic property are delay functions which are based on involutions, i.e., functions that form their own inverse. A concrete example of such a delay function, which is derived from a generalized first-order analog circuit model, reveals that this is not an unrealistic assumption. We prove that, in sharp contrast to what is possible with bounded single-history channels, SPF cannot be solved in bounded time due to the nonexistence of a lower bound on the delay of involution channels, whereas it is easy to provide an unbounded SPF implementation. It hence follows that binary-valued circuit models based on involution channels allow to solve SPF precisely when this is possible in physical circuits. To the best of our knowledge, our model is hence the very first candidate for a model that indeed guarantees faithful glitch propagation.

cs.OH↗

arXiv2013

Unfaithful Glitch Propagation in Existing Binary Circuit Models

We show that no existing continuous-time, binary value-domain model for digital circuits is able to correctly capture glitch propagation. Prominent examples of such models are based on pure delay channels (P), inertial delay channels (I), or the elaborate PID channels proposed by Bellido-Díaz et al. We accomplish our goal by considering the solvability/non-solvability border of a simple problem called Short-Pulse Filtration (SPF), which is closely related to arbitration and synchronization. On one hand, we prove that SPF is solvable in bounded time in any such model that provides channels with non-constant delay, like I and PID. This is in opposition to the impossibility of solving bounded SPF in real (physical) circuit models. On the other hand, for binary circuit models with constant-delay channels, we prove that SPF cannot be solved even in unbounded time; again in opposition to physical circuit models. Consequently, indeed none of the binary value-domain models proposed so far (and that we are aware of) faithfully captures glitch propagation of real circuits. We finally show that these modeling mismatches do not hold for the weaker eventual SPF problem.

cs.OH↗

arXiv2013

Agreement in Directed Dynamic Networks

We study distributed computation in synchronous dynamic networks where an omniscient adversary controls the unidirectional communication links. Its behavior is modeled as a sequence of directed graphs representing the active (i.e. timely) communication links per round. We prove that consensus is impossible under some natural weak connectivity assumptions, and introduce vertex-stable root components as a means for circumventing this impossibility. Essentially, we assume that there is a short period of time during which an arbitrary part of the network remains strongly connected, while its interconnect topology may keep changing continuously. We present a consensus algorithm that works under this assumption, and prove its correctness. Our algorithm maintains a local estimate of the communication graphs, and applies techniques for detecting stable network properties and univalent system configurations. Our possibility results are complemented by several impossibility results and lower bounds for consensus and other distributed computing problems like leader election, revealing that our algorithm is asymptotically optimal.

cs.DC↗

arXiv2013

Counter Attack on Byzantine Generals: Parameterized Model Checking of Fault-tolerant Distributed Algorithms

We introduce an automated parameterized verification method for fault-tolerant distributed algorithms (FTDA). FTDAs are parameterized by both the number of processes and the assumed maximum number of Byzantine faulty processes. At the center of our technique is a parametric interval abstraction (PIA) where the interval boundaries are arithmetic expressions over parameters. Using PIA for both data abstraction and a new form of counter abstraction, we reduce the parameterized problem to finite-state model checking. We demonstrate the practical feasibility of our method by verifying several variants of the well-known distributed algorithm by Srikanth and Toueg. Our semi-decision procedures are complemented and motivated by an undecidability proof for FTDA verification which holds even in the absence of interprocess communication. To the best of our knowledge, this is the first paper to achieve parameterized automated verification of Byzantine FTDA.

cs.LO↗

arXiv2012

Starting a Dialog between Model Checking and Fault-tolerant Distributed Algorithms

Fault-tolerant distributed algorithms are central for building reliable spatially distributed systems. Unfortunately, the lack of a canonical precise framework for fault-tolerant algorithms is an obstacle for both verification and deployment. In this paper, we introduce a new domain-specific framework to capture the behavior of fault-tolerant distributed algorithms in an adequate and precise way. At the center of our framework is a parameterized system model where control flow automata are used for process specification. To account for the specific features and properties of fault-tolerant distributed algorithms for message-passing systems, our control flow automata are extended to model threshold guards as well as the inherent non-determinism stemming from asynchronous communication, interleavings of steps, and faulty processes. We demonstrate the adequacy of our framework in a representative case study where we formalize a family of well-known fault-tolerant broadcasting algorithms under a variety of failure assumptions. Our case study is supported by model checking experiments with safety and liveness specifications for a fixed number of processes. In the experiments, we systematically varied the assumptions on both the resilience condition and the failure model. In all cases, our experiments coincided with the theoretical results predicted in the distributed algorithms literature. This is giving clear evidence for the adequacy of our model. In a companion paper, we are addressing the new model checking techniques necessary for parametric verification of the distributed algorithms captured in our framework.

cs.FL↗

arXiv2012

FATAL+: A Self-Stabilizing Byzantine Fault-tolerant Clocking Scheme for SoCs

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 like metastability. The algorithm, which consists of several concurrent communicating asynchronous state machines, has been implemented in VHDL using Petrify in conjunction with some extensions, and synthetisized for an Altera Cyclone FPGA. An experimental validation of this prototype has been carried out to confirm the skew and clock frequency bounds predicted by the theoretical analysis, as well as the very short stabilization times (required for recovering after excessively many transient failures) achievable in practice.

cs.DC↗

arXiv2011

Fault-tolerant Algorithms for Tick-Generation in Asynchronous Logic: Robust Pulse Generation

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 paper is intended to be part of an attempt striving to overcome this gap between theory and practice for the clock synchronization problem. Solving this task sufficiently well will allow to build a very robust high-precision clocking system for hardware designs like systems-on-chips in critical applications. As our first building block, we describe and prove correct a novel Byzantine fault-tolerant self-stabilizing pulse synchronization protocol, which can be implemented using standard asynchronous digital logic. Despite the strict limitations introduced by hardware designs, it offers optimal resilience and smaller complexity than all existing protocols.

cs.DC↗

arXiv2011

Easy Impossibility Proofs for k-Set Agreement in Message Passing Systems

Despite of being quite similar agreement problems, consensus and general k-set agreement require surprisingly different techniques for proving the impossibility in asynchronous systems with crash failures: Rather than relatively simple bivalence arguments as in the impossibility proof for consensus (= 1-set agreement) in the presence of a single crash failure, known proofs for the impossibility of k-set agreement in systems with at least k>1 crash failures use algebraic topology or a variant of Sperner's Lemma. In this paper, we present a generic theorem for proving the impossibility of k-set agreement in various message passing settings, which is based on a simple reduction to the consensus impossibility in a certain subsystem. We demonstrate the broad applicability of our result by exploring the possibility/impossibility border of k-set agreement in several message-passing system models: (i) asynchronous systems with crash failures, (ii) partially synchronous processes with (initial) crash failures, and (iii) asynchronous systems augmented with failure detectors. In (i) and (ii), the impossibility part is just an instantiation of our main theorem, whereas the possibility of achieving k-set agreement in (ii) follows by generalizing the consensus algorithm for initial crashes by Fisher, Lynch and Patterson. In (iii), applying our technique yields the exact border for the parameter k where k-set agreement is solvable with the failure detector class (Sigma_k,Omega_k), for (1<= k<= n-1), of Bonnet and Raynal. Considering that Sigma_k was shown to be necessary for solving k-set agreement, this result yields new insights on the quest for the weakest failure detector.

cs.DC↗

arXiv2011

Solving k-Set Agreement with Stable Skeleton Graphs

In this paper we consider the k-set agreement problem in distributed message-passing systems using a round-based approach: Both synchrony of communication and failures are captured just by means of the messages that arrive within a round, resulting in round-by-round communication graphs that can be characterized by simple communication predicates. We introduce the weak communication predicate PSources(k) and show that it is tight for k-set agreement, in the following sense: We (i) prove that there is no algorithm for solving (k-1)-set agreement in systems characterized by PSources(k), and (ii) present a novel distributed algorithm that achieves k-set agreement in runs where PSources(k) holds. Our algorithm uses local approximations of the stable skeleton graph, which reflects the underlying perpetual synchrony of a run. We prove that this approximation is correct in all runs, regardless of the communication predicate, and show that graph-theoretic properties of the stable skeleton graph can be used to solve k-set agreement if PSources(k) holds.

cs.DC↗