Question

Construct a regular expression over the alphabet {a,b,c}, in which for the string w; the string length must be an odd number with at least 3 characters. Also, the first and last symbols must be the same. Please give your expression in the shortest possible form.

Answer 1

The regular expression (a|b|c)(a|b|c)*\1 satisfies the criteria of having an odd length string (minimum 3 characters) over the alphabet {a, b, c}, with the first and last characters being the same.

Step-by-step explanation:

A student seeks a regular expression over the alphabet {a, b, c} with specific constraints. The string w which is accepted by this regular expression must have an odd length of at least 3 characters, and the first and last characters of w must be the same. An example of a regular expression that fulfills these requirements could be as follows:

(a|b|c)(a|b|c)*\1

This expression starts and ends with the same character (either 'a', 'b', or 'c'), represented by (a|b|c), followed by zero or more characters (a|b|c)*, ensuring an odd length. The '\1' at the end refers back to the first captured character, thus guaranteeing that the first and last characters are the same. In order to ensure that the string is at least 3 characters long, the middle part of the string can have any characters from the alphabet and is represented by (a|b|c)*, which allows any number of characters to appear in the middle.