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Which of the following decision problems are undecidable?
I. Given NFAs N1 and N2, is L(N1) ∩ L(N2) = Φ?
II. Given a CFG G = (N, Σ, P, S) and a string x ∈ Σ*, does x ∈ L(G)?
III. Given CFGs G1 and G2, is L(G1) = L(G2)?
IV. Given a TM M, is L(M) = Φ?
- I and IV only
- II and III only
- III and IV only
- II and IV only
Correct answer: III and IV only
Solution
Options III and IV are correct because determining if two context-free grammars generate the same language (III) and whether the language of a Turing machine is empty (IV) are both undecidable problems, meaning there is no algorithm that can solve them for all possible inputs.
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#include<stdio.h>
void mystery(int *ptra, int *ptrb) {
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int main() {
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