0
$\begingroup$

If $P=ab$ and $Q=a^*$, how do I use Arden's theorem to determine the regular expression $R$. I'm not sure if I am supposed to just substitute the values of $P$ and $Q$ in the equation $R= Q + RP$. Also how would I use that to check that $R$ satisfies Arden's equation.

$\endgroup$
  • 3
    $\begingroup$ It's not at all clear what you're asking here. Questions should be reasonably self-contained. Could you please explain how R relates to P and Q, and perhaps even give the statement of Arden's theorem (since it's very short)? Thanks. $\endgroup$ – Pseudonym Sep 6 at 23:11
1
$\begingroup$

Arden's theorem states that $A^*\,B$ is the least fixed point of the equation:

$$ X = A\,X\,\cup B$$

and that $A\,B^*$ is the least fixed point of the equation:

$$X = X\,B\,\cup A$$

In your case, $R = Q\,P^* = a^* (a b)^*$.

| cite | improve this answer | |
$\endgroup$

Your Answer

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