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Issue No.07 - July (1969 vol.18)

pp: 652-660

A. Lempel , IEEE

ABSTRACT

A state graph (SG) is a directed graph with exactly one arc issuing from every vertex of the graph. The degree of an SG is the smallest integer d such that at most d, arcs are entering any vertex of the graph. An SG is said to be k-stable if it contains k=1 cycles of unit length (loops) and these are the only cycles of the graph. A k-stable SG with mn vertices and degree d is called a (k, m, n)-SG if m=k, d and if the distance from any vertex to a loop of the graph is at most n.

INDEX TERMS

Feedback shift registers, minimal realization of a stable FSR, sequential machines, state graphs.

CITATION

A. Lempel, "On k-Stable Feedback Shift Registers",

*IEEE Transactions on Computers*, vol.18, no. 7, pp. 652-660, July 1969, doi:10.1109/T-C.1969.222734