This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
On the Lower Bound to the Memory of Finite State Machines
September 1969 (vol. 18 no. 9)
pp. 856-861
A finite state machine (FSM) is said to have finite memory ? if ? is the least integer such that yk= f(Xk, Xk-1,... Xk-?, Yk-1, ... ?k-?) where ykand Xkrepresent the output and input at time k. If no such ? exists, then by convention the memory is said to be infinite. It has been observed [1] that if the memory of a p-nary input, q-nary output n-state minimal nondegenerate FSM is finite, then the memory ? is bounded as follows: Recently, considerable attention has been devoted to the study of the upper bound on ? [2]-[5]. In this paper we examine the lower bound on ?. We show that the lower bound is tight for all positive integers n and certain values of p and q. We also show that when n = 4k, k a positive integer, there exist binary input, binary output minimal FSMs with minimal memory. It will be seen that this is equivalent to showing that for all positive integers ? there exist binary input, binary output minimal FSMs with the maximum number of states n=22?. Finally, we enumerate the equivalence classes of these finite memory machines with memory ? and n = 22?states.
Index Terms:
Finite memory, finite state machines, lower bound on memory, minimal canonical realizations.
Citation:
K. Vairavan, "On the Lower Bound to the Memory of Finite State Machines," IEEE Transactions on Computers, vol. 18, no. 9, pp. 856-861, Sept. 1969, doi:10.1109/T-C.1969.222782
Usage of this product signifies your acceptance of the Terms of Use.