Each relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
- Relation ID
story_undecidable_problem_to_halting_problem_classification- Relation type
- Classification
classification - Direction
- source → target
- Endpoint roles
- source: Has subtype; target: Classified as
- Authored annotation
- has the halting problem as a canonical example
Authored explanation
The halting problem is a specific undecidable decision problem: no total algorithm correctly decides termination for every encoded machine-input pair.
How to interpret this relation type
The target is a member or subtype of the broader source class.
Relation sources
- Turing — On Computable Numbers — On Computable Numbers, with an Application to the Entscheidungsproblem · original research paper · source ID
turing-computable-numbers
This is an authored directed relation from the source endpoint to the target endpoint.
- Relation ID
story_universal_turing_machine_to_halting_problem_canonical_construction- Relation type
- Canonical construction
canonical-construction - Direction
- source → target
- Endpoint roles
- source: Canonically constructs; target: Canonically constructed from
- Authored annotation
- poses termination of encoded simulations
Authored explanation
Encoding machines and inputs permits the decision problem asking whether the universal simulation of a given machine on a given input eventually halts.
How to interpret this relation type
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
Relation sources
- Turing — On Computable Numbers — On Computable Numbers, with an Application to the Entscheidungsproblem · original research paper · source ID
turing-computable-numbers