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8th Annual Symposium on Switching and Automata Theory (SWAT 1967) (1967)
Oct. 18, 1967 to Oct. 20, 1967
pp: 251-254
Various procedures have long been known for synthesizing a sequential machine with a feedback shift-register if each state is to have exactly one assignment; however, these approaches fail if each state is allowed to have more than one assignment. Herein lies the equivalent-state problem. The equivalent-state problem is approached by establishing a relationship between feedback shift-register realizable flow tables and finite memory-span. From this relationship, a necessary and sufficient condition is derived for the realizability of a sequential machine with a feedback shift-register. The concept of the pair-graph is introduced which is used to bound the level and length of the feedback shift-register realization of a sequential machine. From an investigation of the pair-graph, recursive procedures arise which test sequential machines in which each state has L distinct successors for L-level feedback shift-register realizability. The complexity of feedback shift-register synthesis of more general machines is demonstrated.

T. F. Piatkowski and E. L. Lawler, "Generalized state identification problems," 8th Annual Symposium on Switching and Automata Theory (SWAT 1967)(FOCS), Texas, 1967, pp. 251-254.
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