Problem Detail: I’m trying to write a regular expression for some particular license plates. They consist of one up to three capital letters, a hyphen, one up to two capitol letters and one up to four numbers. The license plate should not exceed the 8 symbols. Example: AA-AA123 What I have until now is the following: because there has to be at least one letter before the hyphen, I have this expression for the first letter: $$ P = (Acup B cup…cup Z) $$ For the second letter: $$ D = (Acup B cup…cup Zcup empty) $$ empty indicates the possibility that there could not be a letter. For the numbers is basically almost the same procedure: $$ E = (1cup 2 cup…cup 9) $$ $$ F = (1cup 2 cup…cup 9 cup empty) $$ now for my explicit expression I think the answer would be: $$ K= PDD^* – PDEF^*F^* $$ but I’m not quite sure. I think this means I have 8 symbols, at least one letter before the hyphen but I could have up to three, the hyphen (that is a must), at least one letter after the hyphen but up to two and at least one number but I could have up to 4. Something tells me I have something wrong here, I’m still new in the regular expressions world and I appreciate any help I could get in advance.
Asked By : nubz0r
Answered By : Artemis
As David Richerby pointed out $D^*$ will accept an arbitrary number of letters (including none). If I’m not mistaken you need to take all possible options to achieve not having more than 8 characters. $$ K = ( PDD-PDEF ) cup (PDD-PEFF) cup (PD-PDEFF) cup (PD-PEFFF) cup (P-PDEFFF) $$ This assumes the hyphen is one of the 8 letters and thus does not allow more than 8 letters. Less letters are allowed because of your definitions of $F$ and $D$ including the empty word $varepsilon$. EDIT: added missing cases from commenter.
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