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Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach
, 1998
"... . The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a ..."
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Cited by 75 (15 self)
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. The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving Borel probability measures. Under reasonable conditions, generalized probabilistic bisimilarity can be characterized categorically. Application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation. Keywords. Bisimulation, probabilistic transition system, coalgebra, ultrametric space, Borel measure, final coalgebra. 1 Introduction For discrete probabilistic transition systems the notion of probabilistic bisimilarity of Larsen and Skou [LS91] is regarded as the basic process equivalence. The definition was given for reactive systems. However, Van Glabbeek, Smolka and Steffen s...
Joint sourcechannel turbo decoding of entropycoded sources
 IEEE J. Select. Areas Commun
, 2001
"... Abstract—We analyze the dependencies between the variables involved in the source and channel coding chain. This analysis is carried out in the framework of Bayesian networks, which provide both an intuitive representation for the global model of the coding chain and a way of deriving joint (soft) d ..."
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Cited by 44 (13 self)
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Abstract—We analyze the dependencies between the variables involved in the source and channel coding chain. This analysis is carried out in the framework of Bayesian networks, which provide both an intuitive representation for the global model of the coding chain and a way of deriving joint (soft) decoding algorithms. Three sources of dependencies are involved in the chain: 1) the source model, a Markov chain of symbols; 2) the source coder model, based on a variable length code (VLC), for example a Huffman code; and 3) the channel coder, based on a convolutional error correcting code. Joint decoding relying on the hidden Markov model (HMM) of the global coding chain is intractable, except in trivial cases. We advocate instead an iterative procedure inspired from serial turbo codes, in which the three models of the coding chain are used alternately. This idea of using separately each factor of a big product model inside an iterative procedure usually requires the presence of an interleaver between successive components. We show that only one interleaver is necessary here, placed between the source coder and the channel coder. The decoding scheme we propose can be viewed as a turbo algorithm using alternately the intersymbol correlation due to the Markov source and the redundancy introduced by the channel code. The intermediary element, the source coder model, is used as a translator of soft information from the bit clock to the symbol clock. Index Terms—Bayesian network, data compression, entropy coding, iterative decoding, joint sourcechannel decoding, probabilistic inference, soft decoding, turbo code, variable length code. I.
Markov Nets: Probabilistic Models for distributed and concurrent systems
 IEEE Transactions on Automatic Control
, 2001
"... For distributed systems, i.e. large networked complex systems, there is a drastic difference between a local view and knowledge of the system, and its global view. Distributed systems have local state and time, but do not possess global state and time in the usual sense. In this paper, motivated by ..."
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Cited by 30 (15 self)
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For distributed systems, i.e. large networked complex systems, there is a drastic difference between a local view and knowledge of the system, and its global view. Distributed systems have local state and time, but do not possess global state and time in the usual sense. In this paper, motivated by the monitoring of distributed systems and in particular of telecommunications networks, we develop Markov nets as an extension of Markov chains and hidden Markov models (Hmm) for distributed and concurrent systems. By a concurrent system, we mean a system in which components may evolve independently, with sparse synchronizations. We follow a socalled true concurrency approach, in which neither global state nor global linear time are available. Instead, we use only local states in combination with a partial order model of time. Our basic mathematical tool is that of Petri net unfoldings. Keywords : discrete event systems, stochastic Petri nets, unfoldings. 1 Motivations Distributed network...
Monitoring distributed systems with distributed algorithms
 In Proc of the 2002 IEEE Conf. on Decision and Control, 411–416, Dec. 2002, Las Vegas
"... This paper proposes a framework to process large distributed systems by parts, through distributed algorithms. We consider distributed (discrete event) systems as the combination of elementary components. Each component defines dynamics on several state variables, and the composition is simply defin ..."
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Cited by 12 (6 self)
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This paper proposes a framework to process large distributed systems by parts, through distributed algorithms. We consider distributed (discrete event) systems as the combination of elementary components. Each component defines dynamics on several state variables, and the composition is simply defined by sharing variables. The compound system is asynchronous: each component evolves with its own clock, and exchanges information with its neighbors by means of the shared variables. An interaction graph can be associated to such a compound system: two components are neighbors of each other as soon as they share one (or more) variables. This structure is reminiscent of Bayesian networks, or Markov random fields, which use a graph to display dependencies between random variables. The parallel can actually be pushed quite far. In this paper we show that a large family of modular algorithms developped for Markov fields, in order to solve problems like maximum likelihood state estimation, can be translated into distributed algorithms to monitor large distributed dynamic systems. 1
Approximating Continuous Markov Processes
, 2000
"... Markov processes with continuous state spaces arise in the analysis of stochastic physical systems or stochastic hybrid systems. The standard logical and algorithmic tools for reasoning about discrete (finitestate) systems are, of course, inadequate for reasoning about such systems. In this work we ..."
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Cited by 9 (3 self)
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Markov processes with continuous state spaces arise in the analysis of stochastic physical systems or stochastic hybrid systems. The standard logical and algorithmic tools for reasoning about discrete (finitestate) systems are, of course, inadequate for reasoning about such systems. In this work we develop three related ideas for making such reasoning principles applicable to continuous systems. ffl We show how to approximate continuous systems by a countable family of finitestate probabilistic systems, we can reconstruct the full system from these finite approximants, ffl we define a metric between processes and show that the approximants converge in this metric to the full process, ffl we show that reasoning about properties definable in a rich logic can be carried out in terms of the approximants. The systems that we consider are Markov processes where the state space is continuous but the time steps are discrete. We allow such processes to interact with the environment by syn...
A Petri net approach to fault detection and diagnosis in distributed systems
, 1997
"... : This report presents a new use of safe Petri nets in the field of distributed Discrete Event Dynamic Systems, with application to telecommunication network management. This study has in its long range objectives to provide a generic supervisor, which can be easily distributed on a set of sensors. ..."
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Cited by 7 (5 self)
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: This report presents a new use of safe Petri nets in the field of distributed Discrete Event Dynamic Systems, with application to telecommunication network management. This study has in its long range objectives to provide a generic supervisor, which can be easily distributed on a set of sensors. Petri nets are used to provide both a model and an algorithm in fault management domain. Key features of our approach are 1/ we take advantage of the ability of Petri Nets to model concurrency in distributed systems, 2/ we refuse using the marking graph in our algorithms in order to avoid state explosion and thus rely instead on the socalled partial order semantics of Petri Nets, and, 3/ our algorithms use net unfolding techniques associated with partial order semantics, and extend them to the probabilistic case by providing a generalized Viterbi algorithm. This report is composed of two independent parts. The first one concentrates on application, motivations, and modelling. The second par...