Reachability of fuzzy matrix period

Rok, strany: 1999, 61 - 79

The computational complexity of the matrix period reachability problem (MPR) in a fuzzy algebra $Scr B$ is studied. Given an $n× n$ matrix $A$ with elements in $Scr B$, the problem is to decide whether there is an $n$-vector $x$ such that the sequence of matrix powers $A, A², A³,…$ has the same period length as the sequence $Ax, A²x, A³x,…$ of iterates of $x$. In general, the MPR problem is NP-complete. Two conditions are described, both of which together imply that MPR can be solved in $O(n³)$ time. If only one of the conditions is satisfied, the problem remains NP-complete.

ISO 690:

Gavalec, M., Rote, G. 1999. Reachability of fuzzy matrix period. In Tatra Mountains Mathematical Publications, vol. 16, no.1, pp. 61-79. 1210-3195.

APA:

Gavalec, M., Rote, G. (1999). Reachability of fuzzy matrix period. Tatra Mountains Mathematical Publications, 16(1), 61-79. 1210-3195.