How can I represent the regular language ∑={a,b,c} with a regular expression in such a way that two characters 'b' cannot be next to each other?

Question

The alphabets of a regular language are ∑={a,b,c}

I need create regular expression for:

a.) Accepts strings that do not have two 'b' characters next to each other. example: aabccbaaccb <- allowed aabccbaaccbb <- not allowed

b.) Accepts strings with at least one character 'a' between two characters 'b'. example: babaaaaaab <- allowed babaaaaaabcb <- not allowed

Created regular expression need to be ready for that it can be tested with JFLAP.

Here is what Regular Expression I have already try to create

Answer 1

I think something like this would work:

^[ac]*(?:b$|bc*$|bc*a[ac]*)*$

In testing, it only matches strings where any pair of bs are separated by at least one a, just as the prompt describes.

Answer 2

For task A:

(a+c+ba+bc)*(b+!)

(For some odd reason JFLAP uses ! to represent the empty string, i.e. ϵ)

For task B:

(a+c+bc*a)*(bc*+!)