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HEX : Scaling honeycombs is easier than scaling clock trees
(2016-08-01) Dolev, Danny; Függer, Matthias; Lenzen, Christoph; Perner, Martin; Schmid, Ulrich; Department of Computer Science
We argue that a hexagonal grid with simple intermediate nodes is a robust alternative to buffered clock trees typically used for clock distribution in VLSI circuits, multi-core processors, and other applications that require accurate synchronization: Our HEX grid is Byzantine fault-tolerant, self-stabilizing, and seamlessly integrates with multiple synchronized clock sources, as used in multi-synchronous Globally Synchronous Locally Asynchronous (GALS) architectures. Moreover, HEX guarantees a small clock skew between neighbors even for wire delays that are only moderately balanced. We provide both a theoretical analysis of the worst-case skew and simulation results that demonstrate a very small average skew.
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Synchronous counting and computational algorithm design
(2016-03-01) Dolev, Danny; Heljanko, Keijo; Järvisalo, Matti; Korhonen, Janne H.; Lenzen, Christoph; Rybicki, Joel; Suomela, Jukka; Wieringa, Siert; Department of Computer Science
Consider a complete communication network on n nodes. In synchronous 2-counting, the nodes receive a common clock pulse and they have to agree on which pulses are "odd" and which are "even". Furthermore, the solution needs to be self-stabilising (reaching correct operation from any initial state) and tolerate f Byzantine failures (nodes that send arbitrary misinformation). Prior algorithms either require a source of random bits or a large number of states per node. In this work, we give fast state-optimal deterministic algorithms for the first non-trivial case f=1. To obtain these algorithms, we develop and evaluate two different techniques for algorithm synthesis. Both are based on casting the synthesis problem as a propositional satisfiability (SAT) problem; a direct encoding is efficient for synthesising time-optimal algorithms, while an approach based on counter-example guided abstraction refinement discovers non-optimal algorithms quickly.
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Fault-tolerant algorithms for tick-generation in asynchronous logic : Robust pulse generation
(2014-09-08) Dolev, Danny; Függer, Matthias; Schmid, Ulrich; Lenzen, Christoph; Department of Computer Science
Today's hardware technology presents a new challenge in designing robust systems. Deep submicron VLSI technology introduces 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 article is intended to be part of an attempt striving to bridge over this gap between theory and practice for the clock synchronization problem. Solving this task sufficiently well will allow to build an ultrarobust 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 distributed, Byzantine fault-tolerant, probabilistically self-stabilizing pulse synchronization protocol, called FATAL, that can be implemented using standard asynchronous digital logic: Correct FATAL nodes are guaranteed to generate pulses (i.e., unnumbered clock ticks) in a synchronized way, despite a certain fraction of nodes being faulty. FATAL uses randomization only during stabilization and, despite the strict limitations introduced by hardware designs, offers optimal resilience and smaller complexity than all existing protocols. Finally, we show how to leverage FATAL to efficiently generate synchronized, self-stabilizing, high-frequency clocks. 2014 Copyright held by the Owner/Author.
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Rigorously modeling self-stabilizing fault-tolerant circuits : An ultra-robust clocking scheme for systems-on-chip
(2014-06) Dolev, Danny; Függer, Matthias; Posch, Markus; Schmid, Ulrich; Steininger, Andreas; Lenzen, Christoph; Department of Computer Science
We present the first implementation of a distributed clock generation scheme for Systems-on-Chip that recovers from an unbounded number of arbitrary transient faults despite a large number of arbitrary permanent faults. We devise self-stabilizing hardware building blocks and a hybrid synchronous/asynchronous state machine enabling metastability-free transitions of the algorithm's states. We provide a comprehensive modeling approach that permits to prove, given correctness of the constructed low-level building blocks, the high-level properties of the synchronization algorithm (which have been established in a more abstract model). We believe this approach to be of interest in its own right, since this is the first technique permitting to mathematically verify, at manageable complexity, high-level properties of a fault-prone system in terms of its very basic components. We evaluate a prototype implementation, which has been designed in VHDL, using the Petrify tool in conjunction with some extensions, and synthesized for an Altera Cyclone FPGA.
Verk
Molecular signatures of obstructive sleep apnea in adults : A review and perspective
(2009-04-01) Arnardottir, Erna S.; Mackiewicz, Miroslaw; Gislason, Thorarinn; Teff, Karen L.; Pack, Allan I.; Department of Engineering
The consequences of obstructive sleep apnea (OSA) are largely mediated by chronic intermittent hypoxia and sleep fragmentation. The primary molecular domains affected are sympathetic activity, oxidative stress and infammation. Other affected domains include adipokines, adhesion molecules and molecules that respond to endoplasmic reticulum stress. Changes in molecular domains affected by OSA, assessed in blood and/or urine, can provide a molecular signature for OSA that could potentially be used diagnostically and to predict who is likely to develop different OSA-related comorbidities. High-throughput discovery strategies such as microarrays, assessing changes in gene expression in circulating blood cells, have the potential to fnd new candidates and pathways thereby expanding the molecular signatures for OSA. More research is needed to fully understand the pathophysiological signifcance of these molecular signatures and their relationship with OSA comorbidities. Many OSA subjects are obese, and obesity is an independent risk factor for many comorbidities associated with OSA. Moreover, obesity affects the same molecular pathways as OSA. Thus, a challenge to establishing a molecular signature for OSA is to separate the effects of OSA from obesity. We propose that the optimal strategy is to evaluate the temporal changes in relevant molecular pathways during sleep and, in particular, the alterations from before to after sleep when assessed in blood and/or urine. Such changes will be at least partly a consequence of chronic intermittent hypoxia and sleep fragmentation that occurs during sleep.

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