Try substituting other symbols, which makes it easier to see. 1 for ( and 0 for ) for example.

Then we have

    1010

and

    1001

It depends on your definition of palindrome. Is it 'reads the same forwards or backwards' or is it 'had the same characters in the second half as in the first, but in reverse order'?

You'll find that according to most dictionaries, ()() is the palindrome here.

Unless you're a robot.

Try replacing ( with a and ) with b : abab -> not palindrome abba -> palindrome

For a second I thought you have the most fitting username ever for this discussion, but then I saw that your account has just been created :D