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Maximal Memory Binary Input-Binary Output Finite-Memory Sequential Machines
January 1968 (vol. 17 no. 1)
pp. 67-71
Monroe M. Newborn, Dept. of Elec. Engrg., Ohio State University, Columbus, Ohio.; Dept. of Elec. Engrg., Columbia University, New York, N. Y.
Gill[1] has shown that if there exists a finite-memory n-state sequential machine with finite memory ¿, then ¿ cannot exceed ½n(n-1)¿Nn. He has further shown[2] that there exists an n-state Nn input-binary output machine with memory ¿= Nn for every n. The question of whether a tighter upper bound might be placed on ¿ by the order of the input alphabet was raised by Gill. Massey[3] recently has shown that there exists a ternary input-binary output finite-memory machine with memory ¿=Nn for every n. The primary purpose of this note is to show that for every n there exists an n-state binary input-binary output finite-memory machine with memory ¿= Nn, and thus ¿ is shown not to be limited by the order of the input alphabet. It is shown that for every n there are actually at least two different machines with memory ¿ = Nn. It will also be shown that for every n there exists a binary input-binary output n-state finite-memory machine with ¿ = Nn-1.
Citation:
Monroe M. Newborn, "Maximal Memory Binary Input-Binary Output Finite-Memory Sequential Machines," IEEE Transactions on Computers, vol. 17, no. 1, pp. 67-71, Jan. 1968, doi:10.1109/TC.1968.5008872
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