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Undecidable problem

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Summary

A decision problem for which no algorithm halts on every input with the correct yes-or-no answer.

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Carrier(s)

Axioms / constraints

Canonically induces

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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

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Undecidable problemHalting problem

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

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