Which of the following is true about the Halting Problem?

Question

BlackTom AI · Accepted Answer

When evaluating the Halting Problem, we must assess what each statement claims about its computability and formal language classification.
Option 1: 'It is undecidable' — This is true. The Halting Problem asks whether a given program will halt on a given input, and Alan Turing proved in 1936 that no general algorithm can determine this for all possible program-input pairs. This undecidability is a foundational result in computability theory and means there is no universal halting detector.
Option 2: 'It is decidable' — This is incorrect. If the Halting Problem were decidable, we could construct a machine that always decides whether any program halts, which contradicts Turing's proof of undecidability. The statement ignores the established limit on algorithmic prediction of program behavior.
Option 3: 'It is regular' — This is false. Regular languages are recognized by finite automata and have very limited expressive power. The Halting Problem is a meta-problem about computation itself, not a pattern that can be captured by a regular language, so it cannot be regular in the formal-language sense.
Option 4: 'It is context-free' — This is also false. Context-free languages, recognized by pushdown automata, still cannot encapsulate the Halting Problem's full set of behaviors for all programs and inputs. The Halting Problem requires more computational power than what context-free languages provide, and no single CFG can represent the problem's generality.

COMP30026_2025_SM2 Supplementary or Special Exam: Models of Computation (COMP30026_2025_SM2)- Requires Respondus LockDown Browser

Which of the following is true about the Halting Problem?

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