I'm trying to understand the proof of undecidability of the halting problem. Some resources give a short proof based on a proof by contradiction. There is no mention of diagonalization. But some others also mention diagonalization in the proof. I'm rather confused about the role of diagonalization in this proof. Is it needed? If yes what is its role? Or can the proof be done without utilizing diagonalization?
Asked
Active
Viewed 109 times
1 Answers
5
Unless you found an unusual proof, they're all refutations by contradiction (not "proofs by contradiction", although that is common parlance) and they all are qlso a form of diagonalization: to refute the claim, we assume there were a halting oracle, and derive a contradiction by diagonalizing against the oracle.
You might be getting too hung up with what books call these proofs, and whether they bother to mention words "contradiction" and "diagonalization". They should all be the same proof, if we discount minor details in presentation.
Andrej Bauer
- 31,657
- 1
- 75
- 121