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IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 2008 E91-A(5):1278-1282; doi:10.1093/ietfec/e91-a.5.1278
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Copyright © 2008 The Institute of Electronics, Information and Communication Engineers

Regular Section -- Letters -- Systems and Control

Efficient Calculation of the Transition Matrix in a Max-Plus Linear State-Space Representation

Hiroyuki GOTO1

1 The author is with Nagaoka University of Technology, Nagaoka-shi, 940-2188 Japan. E-mail: hgoto{at}kjs.nagaokaut.ac.jp


  Abstract

This research considers an efficient method for calculating the transition matrix in an MPL (Max-Plus Linear) state-space representation. This matrix can be generated by applying the Kleene star operator to an adjacency matrix. The proposed method, based on the idea of a topological sort in graph theory and block splitting, is able to calculate the transition matrix efficiently.

Key Words: max-plus linear representation, directed acyclic graph, adjacency matrix, Kleene star, topological sort

Manuscript received September 10, 2007. Manuscript revised January 30, 2008.


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