variable-order markov models

While a simple Markov model only uses the last state/token to predict the next one, a variable-order Markov model may use several past states. For example a third-order Markov model, gives the probabilty of the state S_t as a function of the last three states:
      P(S_t=s)   =   f(s_t-1,s_t-2,s_t-3)

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