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Maximal Memory Binary InputBinary Output FiniteMemory Sequential Machines
January 1968 (vol. 17 no. 1)
pp. 6771
ASCII Text  x  
Monroe M. Newborn, "Maximal Memory Binary InputBinary Output FiniteMemory Sequential Machines," IEEE Transactions on Computers, vol. 17, no. 1, pp. 6771, January, 1968.  
BibTex  x  
@article{ 10.1109/TC.1968.5008872, author = {Monroe M. Newborn}, title = {Maximal Memory Binary InputBinary Output FiniteMemory Sequential Machines}, journal ={IEEE Transactions on Computers}, volume = {17}, number = {1}, issn = {00189340}, year = {1968}, pages = {6771}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1968.5008872}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Maximal Memory Binary InputBinary Output FiniteMemory Sequential Machines IS  1 SN  00189340 SP67 EP71 EPD  6771 A1  Monroe M. Newborn, PY  1968 VL  17 JA  IEEE Transactions on Computers ER   
Gill^{[1]} has shown that if there exists a finitememory nstate sequential machine with finite memory ¿, then ¿ cannot exceed ½n(n1)¿Nn . He has further shown^{[2]} that there exists an nstate Nn inputbinary 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 inputbinary output finitememory machine with memory ¿=Nn for every n. The primary purpose of this note is to show that for every n there exists an nstate binary inputbinary output finitememory 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 inputbinary output nstate finitememory machine with ¿ = Nn 1.
Citation:
Monroe M. Newborn, "Maximal Memory Binary InputBinary Output FiniteMemory Sequential Machines," IEEE Transactions on Computers, vol. 17, no. 1, pp. 6771, Jan. 1968, doi:10.1109/TC.1968.5008872
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