Abstract
We show how some graph theoretical arguments may be used to reduce the complexity of the computation of the steady-state distribution of Markov chain. We consider the directed graph associated to a Markov chain derived from a Stochastic Automata Network (SAN). The structural properties of the automata are used to establish new various results. First, we establish the complexity of the resolution for Stochastic Automata Networks with a sparse matrix representation of the automata. This results are used to compare simple SAN (i.e. without functions) with methods which generates a sparse representation of Markov chains (i.e. Markovian Petri Nets for instance) on some examples.
Then, we show how to apply state reduction techniques on a chain associated to a SAN. We present an algorithm to solve the steady-state equations and we prove its complexity. Finally, we extend our algorithm to allow the semi-parametric analysis of Stochastic Automata Networks.
1This work is partially supported by a grant from CNRS, project Aξ.
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© 1995 Springer Science+Business Media New York
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Fourneau, JM., Quessette, F. (1995). Graphs and Stochastic Automata Networks. In: Stewart, W.J. (eds) Computations with Markov Chains. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2241-6_14
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DOI: https://doi.org/10.1007/978-1-4615-2241-6_14
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