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Undecidable problem

In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly determines whether an arbitrary program…

Standards, Examples of undecidable statements & Relationship with Gödel's incompleteness theorem

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Examples of undecidable statements

Deductive systemComputable functionFormal systemIndependentTruth value
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Relationship with Gödel's incompleteness theorem

Gödel's incompleteness theoremsAxiomatizationSoundConsistencyCorollary
8 related topics

Background

Prime numberStringsFormal languageNatural numbersGödel numbering
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Examples of undecidable problems

LogicAbstract machinesTopologyUncountablyInfinite length
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Overview

Background

Relationship with Gödel's incompleteness theorem

Examples of undecidable problems

Examples of undecidable statements

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Undecidable problem

Nodes75
Edges74
Triples3
Avg. degree1.97
Density0.026667
Components1

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Undecidable problem

Top relations

related to Examples of undecidable problems · 2
Undecidable problem → Since, Undecidable
is a · 1
Undecidable problem → decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer

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Important terminology

problem undecidable theorem algorithm theory set proved decision statements numbers halting natural statement incompleteness sense whether axiomatization logic system gödel's

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Undecidable problemis adecision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer0.90text
Undecidable problemrelated to Examples of undecidable problemsUndecidable0.60section
Undecidable problemrelated to Examples of undecidable problemsSince0.60section

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