Partial word

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A partial word is a string that may contain a number of "do not know" or "do not care" symbols i.e. placeholders in the string where the symbol value is not known or not specified. More formally, a partial word is a partial function u: \{ 0, \ldots, n-1 \} \rightarrow A where A is some finite alphabet. If u(k) is not defined for some  k \in \{ 0, \ldots, n-1 \} then the unknown element at place k in the string is called a "hole". In regular expressions (following the POSIX standard) a hole is represented by the metacharacter ".". For example, aab.ab.b is a partial word of length 8 over the alphabet A ={a,b} in which the fourth and seventh characters are holes.[1]

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  1. ^ Algorithmic Combinatorics on Words REU