Variable-order Markov model: Difference between revisions

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==Definition==
Let {{mvar|A}} be a state space (finite [[Alphabet (formal languages)|alphabet]]) of size <math>|A|</math>.
 
Consider a sequence with the [[Markov property]] <math>x_1^{n}=x_1x_2\dots x_n</math> of {{mvar|n}} realizations of [[random variable]]s, where <math> x_i\in A</math> is the state (symbol) at position {{mvar|i}} <math>\scriptstyle (1 \le i \le n)</math>, and the concatenation of states <math>x_i</math> and <math>x_{i+1}</math> is denoted by <math>x_ix_{i+1}</math>.