Question

4. (4 points) Bonus question Let $\Sigma$ be an alphabet, and $f(A, B) = \{w \in \Sigma^* | \exists x, y, z, t \in \Sigma^*. w = xy = zt \land x \in A \land z \in B\}$. Show that regular languages are closed under $f$.

          4. (4 points) Bonus question Let $\Sigma$ be an alphabet, and
$f(A, B) = \{w \in \Sigma^* | \exists x, y, z, t \in \Sigma^*. w = xy = zt \land x \in A \land z \in B\}$.
Show that regular languages are closed under $f$.

$4. (4 points) Bonus question Let Σ be an alphabet, and f(A, B) = {w ∈Σ^* | ∃ x, y, z, t ∈Σ^*. w = xy = zt x ∈ A z ∈ B}. Show that regular languages are closed under f.$

Added by Kathryn A.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Thanks for your feedback!

(4 points) Bonus question: Let Σ be an alphabet, and f(A,B) = {w in Σ* | there exists x, y, z, t in Σ* such that w = xy = zt and x in A and z in B}. Show that regular languages are closed under f. 4. (4 points) Bonus question: Let Z be an alphabet, and f(A,B) = {w ∈ Z* | ∃x, y, z, t ∈ Z*. w = xy = zt ∧ x ∈ A ∧ z ∈ B} Show that regular languages are closed under f.