1
$\begingroup$

According to Arden's rule, the language equation $X= AX\cup B$, with unknown $X$, has the solution $X=A^*B$, provided $A$ does not contain the empty string.

My question: what is the problem with the empty string here? Can you illustrate this with a concrete example (which lacks in Wikipedia on this topic).

$\endgroup$
2
$\begingroup$

Consider, for instance, $A = \{ \varepsilon \}$. Then $X = AX$, so $X = AX \cup B$ holds for any $X$ with $B \subseteq X$.

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

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.