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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=<pr align="c">i=1N ni×<sum align="c">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