finite automata - Moore Machines with n states -


i working on end of chapter question regarding how many different moore machines there n states. n = number of states, m = number of input letters, , q = number of output characters, correct there n*q^m possible machines? reasoning each state, each input has possibility lead 1 of give output characters.

a moore machine consists of:

  • set of states s (n)
  • start state s0
  • input alphabet sigma (m)
  • output alphabet (q)
  • transition function (s x sigma -> s)
  • output function (s -> a)

the number of states , input/output-characters given.

for start state there n possibilities.

for transition function, there |s| ^ (|s| * |sigma|) = n^(n*m) different variants.

finally, there |a| ^ |s| = q^n output functions

this yields in total n^(n*m+1) * q^n different moore machines.


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