Discussion
Which of the following problems is undecidable ?
Answer: B
The undecidable problem is the halting problem for Turing machines.
Turing proved in 1936 that no algorithm can decide, for every machine and input, whether that Turing machine halts. The proof is by diagonalisation: a supposed decider could be used to build a machine that halts exactly when the decider says it does not.
The other three are decidable. Membership in a regular language is checked by running a DFA. Emptiness of a finite automaton is checked by seeing whether any accepting state is reachable. Two DFAs are equivalent if their minimised forms are the same.
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