Réseaux d'Automates Stochastiques : Génération de l'espace d'états atteignables et Multiplication vecteur-descripteur pour une sémantique en temps discret

Afonso Henrique Correa de Sales 1
1 MESCAL - Middleware efficiently scalable
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
Abstract : This thesis presents methods and algorithms for the performance evaluation of large state space models described by high-level formalisms. Among the various formalisms we use Stochastic Automata Networks (SAN) formalism. SAN formalism is dedicated to modeling very large systems by the composition of its subsystems (automata), where these automata interact with each other by synchronizing events or functional rates and probabilities. The state space explosion of a model is a common problem when computing the reachable state space of complex systems. In the first part of this thesis, we propose reachable state space generation methods of structured models which use functional rates (general state dependant rates) and probabilities. We use Multi-valued Decision Diagrams (MDD) to store sets of reachable spaces and SAN formalism to describe structured models. MDD is a multilevel data structure which efficiently manipulates a extremely large state spaces. Regarding state-of-the-art generation methods, our methods allow to construct a huge reachable state space of a model which uses functional rates and probabilities. The methods are tested on some models in order to illustrate this contribution. In the second part, we are interested in the solution of a discrete time SAN model whose transition matrix is represented by a tensor formula (called discrete descriptor). For this purpose, we present the Complex Tensor Algebra (XTA) adapted to the parallel composition of the discrete time SANs in order to represent the discrete descriptor and we prove some properties that are the basis for iterative methods for solving the Markov chain associated to the SAN model. Representing a SAN model by a descriptor is a compact way to describe the transitions among global states of the model: we replace a description in a product space by a single tensor product on factors that describe what happens on a single dimension (one automaton of the SAN model). In order to take advantage of this representation, we present a vector-descriptor product method which performs the multiplication of a probability vector and the discrete descriptor. This method aims at exploiting the properties of the complex tensor product so that the multiplication by an operator on the product space is replaced by a series of operations that manipulate data on the size of an automaton (and for all automata).
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https://tel.archives-ouvertes.fr/tel-00436020
Contributor : Afonso Henrique Correa de Sales <>
Submitted on : Wednesday, November 25, 2009 - 5:13:34 PM
Last modification on : Thursday, October 11, 2018 - 8:48:02 AM
Long-term archiving on : Thursday, June 17, 2010 - 10:06:09 PM

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  • HAL Id : tel-00436020, version 1

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Afonso Henrique Correa de Sales. Réseaux d'Automates Stochastiques : Génération de l'espace d'états atteignables et Multiplication vecteur-descripteur pour une sémantique en temps discret. Modélisation et simulation. Institut National Polytechnique de Grenoble - INPG, 2009. Français. ⟨tel-00436020v1⟩

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