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Decision problem

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Summary

A yes-or-no problem represented by a set of finite inputs whose membership is to be decided.

Record metadata

Carrier(s)

Data

Canonically induces

Concept sources

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Decision problemDecidable problem

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

A decision problem is decidable when some algorithm halts with the correct answer on every input.

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

Decision problemMany-one reduction

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

A many-one reduction supplies a total computable translation of instances so that one answer to the target decision problem decides the original instance without adaptive oracle queries.

How to interpret this relation type

Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.

Relation sources

Decision problemUndecidable problem

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

An undecidable problem is a decision problem for which no total algorithm returns the correct yes-or-no answer on every encoded instance.

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