找到正则表达式 (a|b)*ab(a|b)* 的补码

Question

There's a question on my exercise sheet to find the complement of r = (a|b)*ab(a|b)*

I've come up with a solution, but I'm not sure if it's correct. Please help me to check, and correct my errors.

Answer 1

I'm assuming that a and b are the only allowed symbols.

Your original expression matches any string that contains ab . The complement is any string that does not contain ab . In other words if there is an a the next character must be another a or the end of the string. If a b occurs it must be before all a s.

So that gives the result:

b*a*

I think your expression is equivalent to this.

Answer 2

The given RE states the language having substring ab at least once The complement of the same would be ..language accepting no substring ab

Hence b*a* is the correct answer