### Efficient descriptor-vector multiplications in stochastic automata networksEfficient descriptor-vector multiplications in stochastic automata networks

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 Author Fernandes, Paulo ♦ Plateau, Brigitte ♦ Stewart, William J. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1998 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Markov chains ♦ Generalized tensor algebra ♦ Stochastic automata networks ♦ Vector-descriptor multiplication 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 rN=i=1N ni×i=1N ni is the number of states in the $\textit{i}th$ automaton and $\textit{N}$ 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. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1998-05-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 45 Issue Number 3 Page Count 34 Starting Page 381 Ending Page 414

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Source: ACM Digital Library