Issue No. 01 - January (1968 vol. 17)
Monroe M. Newborn , Dept. of Elec. Engrg., Ohio State University, Columbus, Ohio.; Dept. of Elec. Engrg., Columbia University, New York, N. Y.
Gill<sup></sup> has shown that if there exists a finite-memory n-state sequential machine with finite memory ¿, then ¿ cannot exceed ½n(n-1)¿N<inf>n</inf>. He has further shown<sup></sup> that there exists an n-state N<inf>n</inf> input-binary output machine with memory ¿= N<inf>n</inf> 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<sup></sup> recently has shown that there exists a ternary input-binary output finite-memory machine with memory ¿=N<inf>n</inf> 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 ¿= N<inf>n</inf>, 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 ¿ = N<inf>n</inf>. It will also be shown that for every n there exists a binary input-binary output n-state finite-memory machine with ¿ = N<inf>n</inf>-1.
M. M. Newborn, "Maximal Memory Binary Input-Binary Output Finite-Memory Sequential Machines," in IEEE Transactions on Computers, vol. 17, no. , pp. 67-71, 1968.