A Note on the Linear Space Automata Stability Problem

Paz et al. [1] have revealed the necessary and sufficient conditions for a linear automaton to be strongly approximable. In this paper, we extend their theory to a linear space automaton [2], i.e., a linear system with more than one linear mapping, to obtain a necessary and sufficient condition that it is strongly stable.

[1]  Alston S. Householder,et al.  The Theory of Matrices in Numerical Analysis , 1964 .

[2]  Yasuyoshi Inagaki,et al.  Some Aspects of Linear Space Automata , 1972, Inf. Control..

[3]  Azaria Paz,et al.  Linear Automata Approximation Problem , 1974, IEEE Transactions on Computers.

[4]  Some Notes on Stability Problems of Probabilistic Automata , 1971 .

[5]  Azaria Paz,et al.  Introduction to Probabilistic Automata , 1971 .

[6]  Azaria Paz,et al.  Some aspects of Probabilistic Automata , 1966, Inf. Control..

[7]  Michael Rabinovich,et al.  Linear Automata - Approximation Problem (Extended Abstract) , 1972, International Colloquium on Automata, Languages and Programming.