Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm trying to prove that two regular expressions are equivalent. I mean prove in the rigorous sense of the word (i.e. this is a legit proof).

The process is to show that R1 is a subset of R2, and then show R2 is a subset of R1. I'm a bit stuck on moving forward with my problem. Any help would be sweet.

$R_1 = \epsilon + (0+1)^{*}1$
$R_2 = (0^{*}1)^{*}$


share|cite|improve this question

Hint: Show that any string that follows the spec of $R_1$ lies in $R_2$, and vice versa.

Another hint: $R_1$ clearly describes the set of all strings that end with $1$, plus the empty string. Now show that (a) all strings in $R_2$ have this property, (b), every such string can be written in a form that shows that it belongs to $R_2$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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