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The VOM model of maximal order 2 can approximate the above string using ''only'' the following five [[conditional probability]] components: {{math|Pr(''a'' {{!}} ''aa'') {{=}} 0.5}}, {{math|Pr(''b'' {{!}} ''aa'') {{=}} 0.5}}, {{math|Pr(''c'' {{!}} ''b'') {{=}} 1.0}}, {{math|Pr(''a'' {{!}} ''c''){{=}} 1.0}}, {{math|Pr(''a'' {{!}} ''ca'') {{=}} 1.0}}.
In this example, {{math|Pr(''c'' {{!}} ''ab'') {{=}} Pr(''c'' {{!}} ''b'') {{=}} 1.0}}; therefore, the shorter context {{math|''b''}} is sufficient to determine the next character. Similarly, the VOM model of maximal order 3 can generate the string exactly using only five conditional probability components, which are all equal to 1.0.
To construct the [[Markov chain]] of order 1 for the next character in that string, one must estimate the following 9 conditional probability components: {{math|Pr(''a'' {{!}} ''a'')}}, {{math|Pr(''a'' {{!}} ''b'')}}, {{math|Pr(''a'' {{!}} ''c'')}}, {{math|Pr(''b'' {{!}} ''a'')}}, {{math|Pr(''b'' {{!}} ''b'')}}, {{math|Pr(''b'' {{!}} ''c'')}}, {{math|Pr(''c'' {{!}} ''a'')}}, {{math|Pr(''c'' {{!}} ''b'')}}, {{math|Pr(''c'' {{!}} ''c'')}}. To construct the Markov chain of order 2 for the next character, one must estimate 27 conditional probability components: {{math|Pr(''a'' {{!}} ''aa'')}}, {{math|Pr(''a'' {{!}} ''ab'')}}, {{math|…}}, {{math|Pr(''c'' {{!}} ''cc'')}}. And to construct the Markov chain of order three for the next character one must estimate the following 81 conditional probability components: {{math|Pr(''a'' {{!}} ''aaa'')}}, {{math|Pr(''a'' {{!}} ''aab'')}}, {{math|…}}, {{math|Pr(''c'' {{!}} ''ccc'')}}.
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