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Algebraic techniques for timed systems
 in CONCUR'98 Concurrency Theory, 9th International Conference
, 1998
"... A b s t r a c t. Performance evaluation is a central issue in the design of complex realtime systems. In this work, we propose an extension of socalled "MaxPlus " algebraic techniques to handle more realistic types of realtime systems. In particular, our framework encompasses g ..."
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A b s t r a c t. Performance evaluation is a central issue in the design of complex realtime systems. In this work, we propose an extension of socalled &quot;MaxPlus &quot; algebraic techniques to handle more realistic types of realtime systems. In particular, our framework encompasses graph or partial order automata, and more generally abstract models of realtime computations (including synchronous programs running over distributed architectures). To achieve this, we introduce a new dioid of partially commutative power series (transductions), whose elements encode timed behaviors. This formalism extends the traditional representation of timed event graphs by (rational) commutative transfer series with coefficients in the MaxPlus semiring. We sketch how this framework can be used to symbolically solve several problems of interest, related to realtime systems. Then we illustrate the use of this framework to encode a nontrivial mixed formalism of dataliow diagrams and automata. 1 M o t i v a t i o n s
Series Expansions of Lyapunov Exponents and Forgetful Monoids
, 2000
"... We consider Lyapunov exponents of random iterates of monotone homogeneous maps. We assume that the images of some iterates are lines, with positive probability. Using this memoryloss property which holds generically for random products of matrices over the maxplus semiring, and in particular, for ..."
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We consider Lyapunov exponents of random iterates of monotone homogeneous maps. We assume that the images of some iterates are lines, with positive probability. Using this memoryloss property which holds generically for random products of matrices over the maxplus semiring, and in particular, for Tetrislike heaps of pieces models, we give a series expansion formula for the Lyapunov exponent, as a function of the probability law. In the case of rational probability laws, we show that the Lyapunov exponent is an analytic function of the parameters of the law, in a domain that contains the absolute convergence domain of a partition function associated to a special "forgetful" monoid, defined by generators and relations.
Series Expansions of Lyapunov Exponents and
, 2000
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.