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Transient Behavior of Distributed Algorithms and Digital Circuit Models

Thomas Nowak 1 
1 COMETE - Concurrency, Mobility and Transactions
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : The overall theme of the thesis is the transient behavior of certain distributed systems. The results can be grouped into three different categories: Transients of max-plus matrices and linear systems, convergence of asymptotic consensus systems, and glitch modeling in digital circuits. For max-plus algebra, the results are upper bounds on the transient (coupling time) of max-plus matrices and systems. They strictly improve all existing transience bounds. An account of the impact of these bounds in applications is given. The proofs mainly consist of walk reduction and completion procedures. For critical indices, sharper bounds are possible. In fact, they turn out to be independent of the specific weights, and to only depend on the structure of the matrix's digraph and its critical digraph. They are also strict generalizations of the Boolean transience bounds in non-weighted digraphs by the likes of Wielandt or Dulmage and Mendelsohn. For asymptotic consensus, i.e., a set of agents possessing a real value each and repeatedly updating it by forming weighted averages of its neighbors' values, the thesis strengthens certain upper bounds on the rate of convergence and shows new convergence results for the case of non self-confidence, i.e., agents possibly disregarding their own value. Asymptotic consensus can be described by a non time-homogeneous linear system in classical algebra. The results here are typically in completely dynamic networks. The thesis also presents a worst-case example that shows that exponentially large convergence time is possible even in static networks; meaning that the worst case convergence time in large classes of dynamic networks is actually achieved with a completely static one. The last part of the thesis is about glitch propagation in digital circuits. More specifically, it is about discrete-value continuous-time models for digital circuits. These models are used in hardware design tool chains because they are much faster than numerically solving the differential equations for timing simulations. However, as is shown in the thesis, none of the existing discrete-value models can correctly predict the occurrence of glitches (short pulses) in the output signal of circuits. Moreover, the thesis proposes a new discrete-value model and proves analytically that it does not share the same characteristics with the existing models that prevented them to correctly predict glitches.
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Submitted on : Saturday, September 6, 2014 - 9:03:56 AM
Last modification on : Thursday, January 20, 2022 - 5:26:32 PM
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  • HAL Id : pastel-01061470, version 1



Thomas Nowak. Transient Behavior of Distributed Algorithms and Digital Circuit Models. Distributed, Parallel, and Cluster Computing [cs.DC]. Ecole Polytechnique X, 2014. English. ⟨pastel-01061470⟩



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