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# Efficient Descriptor-Vector Multiplications in Stochastic Automata Networks

1 APACHE - Parallel algorithms and load sharing
ID-IMAG - Informatique et Distribution, Inria Grenoble - Rhône-Alpes, UJF - Université Joseph Fourier - Grenoble 1
Abstract : This paper examines numerical issues in computing solutions to networks of stochastic automata. It is well-known that when the matrices that represent the automata contain only constant values, the cost of performing the operation basic to all iterative solution methods, that of matrix-vector multiply, is given by $\rho_N = \prod_{i=1}^N n_i \times \sum_{i=1}^N n_i ,$ where $n_i$ is the number of states in the $i^{th}$ automaton and $N$ is the number of automata in the network. We introduce the concept of a generalized tensor product and prove a number of lemmas concerning this product. The result of these lemmas allows us to show that this relatively small number of operations is sufficient in many practical cases of interest in which the automata contain functional and not simply constant transitions. Furthermore, we show how the automata should be ordered to achieve this.
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https://hal.inria.fr/inria-00073764
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Submitted on : Wednesday, May 24, 2006 - 1:42:36 PM
Last modification on : Friday, February 4, 2022 - 3:09:22 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:57:27 PM

### Identifiers

• HAL Id : inria-00073764, version 1

### Citation

Paulo Fernandes, Brigitte Plateau, William J. Stewart. Efficient Descriptor-Vector Multiplications in Stochastic Automata Networks. [Research Report] RR-2935, INRIA. 1996. ⟨inria-00073764⟩

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