Question: Prove that the following two languages are undecidable. a. OVERLAP CFG = {G,H| G and H are CFGs where L(G) L(H) }. Adapt
Prove that the following two languages are undecidable.
a. OVERLAPCFG = {⟨G,H⟩| G and H are CFGs where L(G) ∩ L(H) ≠ ⌀}.
Adapt the hint in Problem 5.21.
b. PREFIX-FREECFG = {⟨G⟩| G is a CFG where L(G) is prefix-free}.
Problem 5.21.
Let AMBIGCFG = {⟨G⟩| G is an ambiguous CFG}. Show that AMBIGCFG is undecidable. Use a reduction from PCP. Given an instance
of the Post Correspondence Problem, construct a CFG G with the rules
where a1, . . . , ak are new terminal symbols. Prove that this reduction works.
tk P =
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