1
$\begingroup$

Does the Kleene star distribute over each element? Is this true: $(0+1)^* = (0^* + 1^*)$?

$\endgroup$
  • 6
    $\begingroup$ Interesting question. Have you tried a few examples? Have you tried proving the quality? Is 01 in $0^*+1^*$? $\endgroup$ – Apass.Jack Mar 22 at 22:02
3
$\begingroup$

You can verify that $010$ is in $(0+1)^*$ but not in $(0^* + 1^*)$. Therefore, $(0 + 1)^* \neq (0^* + 1^*)$.

$\endgroup$
2
$\begingroup$

I believe this makes more sense:

$$ (0+1)^* = (0^*1^*)^* $$

$0^* + 1^*$ would limit the amount of strings covered.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.