In some implementations of “regular expressions,” the notations \1, \2, and so on can occur in a search pattern. For example, consider the search pattern ^([a-zA-Z]).*\1$. Here, \1 represents a recurrence of the same substring that matched [a-zA-Z], the part of the pattern between the first pair of parentheses. The entire pattern, therefore, will match a line of text that begins and ends with the same letter. Using this notation, write a pattern that matches all strings in the language L = {a n ban | n ≥ 0}. (Later in this chapter, we will see that L is not a regular language, so allowing the use of \1 in a “regular expression” means that it’s not really a regular expression at all! This notation can add a real increase in expressive power to the patterns that contain it.)
Note that here, I have used some general rules that are abided by the students who learn regular expressions, besides the rules given in the question.
Also, note that I have tried to explain some of those rules above.
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