Question

Generate a constrained Regular Expression for the language that is described by the following: All constraints must apply to the same regular expression.

1) all strings MUST begin with at least one 'a' character
2)all strings must end with exactly one 'a'
3)between the 'a' characters are an unknown number of 'b','c' and 'd' characters
4)the number of 'c' characters are atleast one
5)the number of 'b' characters are exactly the same as the number of 'd' characters

Answer 1

A suitable constrained Regular Expression meeting the mentioned criteria is 'a(bd)*c(b|d|bd)*a', ensuring that all strings start and end with 'a', contain at least one 'c', and have an equal number of 'b' and 'd' characters.

Step-by-step explanation:

The student is seeking to create a constrained Regular Expression that meets several specific conditions related to the composition of the strings it accepts. According to the constraints provided, the strings must begin with at least one 'a' character and must end with exactly one 'a'. In between, there can be an unknown number of 'b', 'c', and 'd' characters, with the additional constraints that there must be at least one 'c' and the number of 'b' characters must match the number of 'd' characters exactly. A possible Regular Expression that satisfies all these conditions is:

a(bd)*c(b|d|bd)*a

This Regular Expression starts with 'a' to satisfy the first constraint. The (bd)* part allows for any number of 'b' and 'd' pairs to satisfy the constraint that their numbers should be equal. The 'c' in the middle ensures at least one 'c' is present. Following the 'c', the (b|d|bd)* part allows for additional 'b's and 'd's, maintaining the requirement that they be in equal number. Finally, the Regular Expression ends with 'a' to comply with the second constraint that the string ends with exactly one 'a'.