Why it matters

Halting problem is foundational undecidability. Understanding shapes computability.

Advertisement

The architecture

Turing's diagonal argument.

Suppose H decides halting.

Construct D that halts iff H says D doesn't halt.

Contradiction.

Halting undecidability proofSuppose Hdecides haltingConstruct Dusing HContradictionH can't decide DDiagonal argument; foundation for Rice's theorem + reductions to prove other undecidables
Halting problem.
Advertisement

How it works end to end

Turing 1936.

Reductions from halting prove other undecidability.

Practical: bounded model checking, static analysis.