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The VOM model of maximal order 2 can approximate the above string using ''only'' the following four [[conditional probability]] components {Pr(a|aa)=0.5, Pr(b|aa)=0.5, Pr(c|b)=1.0, Pr(a|c)= 1.0}. In this example, Pr(c|ab)=Pr(c|b)=1.0, therefore, the shorter context b is sufficient to determine the future state. Similarly, the VOM model of maximal order 3 can approximate the string using only four [[conditional probability]] components.
To construct the [[Markov chain]] of order 1 for the next character in this sequence, one needs to estimate the following 9 [[conditional probability]] components {Pr(a|a), Pr(a|b), Pr(a|c), Pr(b|a), Pr(b|a), Pr(b|a), Pr(c|a), Pr(c|a), Pr(c|a)}.
To construct the [[Markov chain]] of order 2 for the next character in this sequence, one needs to estimate the following 27 [[conditional probability]] components {Pr(a|aa), Pr(a|ab), …, Pr(c|cc)}.
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