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Efficient descriptor-vector multiplications in stochastic automata networks. (English) Zbl 1065.68578
Summary: 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 multiplication, is given by \(\rho_N=\prod^N_{i=1}n_i\times\sum^N_{i=1}n_i\), 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.
Reviewer: Reviewer (Berlin)

MSC:
68Q45 Formal languages and automata
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
65F10 Iterative numerical methods for linear systems
Software:
PEPS
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