Partial word

A partial word is a string that may contain a number of "do not know" or "do not care" symbols. More formally, it is a partial function $u:\; rightarrow\; A$ where $A$ is some finite alphabet. If $i\; in$ but u(i) is not defined then it is called a "hole."

http://www.uncg.edu/mat/reu/index.html

Notes