# Prove that the following two languages are undecidable. a.

**Chapter , Problem 5.32**

(choose chapter or problem)

Prove that the following two languages are undecidable.

a. \(O V E R L A P_{\mathrm{CFG}}=\{\langle G, H\rangle \mid G \text { and } H \text { are CFGs where } L(G) \cap L(H) \neq \emptyset\}\).

(Hint: Adapt the hint in Problem 5.21.)

b. \(P R E F I X-F R E E_{\mathrm{CFG}}=\{\langle G\rangle \mid G \text { is a CFG where } L(G) \text { is prefix-free }\}\)

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