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Decidable: meaning, definitions and examples

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decidable

[ dɪˈsaɪdəbl ]

Adjective

^{Context #1 | Adjective}

computing

Capable of being decided by an algorithm or a formal proof.

Synonyms

computable, solvable.

Which Synonym Should You Choose?

Word	Description / Examples
decidable	Used in mathematics and logic to describe a problem or a question that can be definitively resolved with a yes or no answer. In formal logic, a theory is considered decidable if there is an algorithm that can determine the truth or falsity of any statement in that theory. The problem of whether a given number is prime is decidable.
computable	Generally used in computer science to describe a function or problem that can be solved using an algorithm within finite time and resources. A function is computable if there exists a Turing machine that can compute the function's value for any valid input. Cryptographic algorithms rely on the fact that certain problems are not computable within a reasonable amount of time.
solvable	Used to describe a problem for which a solution exists, irrespective of the method to find it, more commonly in everyday language or practical situations. The issue of climate change is complex, but it is solvable with the right mix of technology and policy. A good detective will tell you that most criminal cases are solvable with enough evidence.

Word

Description / Examples

decidable

Used in mathematics and logic to describe a problem or a question that can be definitively resolved with a yes or no answer.

In formal logic, a theory is considered decidable if there is an algorithm that can determine the truth or falsity of any statement in that theory.
The problem of whether a given number is prime is decidable.

computable

Generally used in computer science to describe a function or problem that can be solved using an algorithm within finite time and resources.

A function is computable if there exists a Turing machine that can compute the function's value for any valid input.
Cryptographic algorithms rely on the fact that certain problems are not computable within a reasonable amount of time.

solvable

Used to describe a problem for which a solution exists, irrespective of the method to find it, more commonly in everyday language or practical situations.

The issue of climate change is complex, but it is solvable with the right mix of technology and policy.
A good detective will tell you that most criminal cases are solvable with enough evidence.

Examples of usage

Whether a problem is decidable or undecidable has important implications in computer science.
In the theory of computation, a language is decidable if there exists an algorithm that can determine whether a given input string belongs to the language.

Translations

Translations of the word "decidable" in other languages:

🇵🇹 decidível

🇮🇳 निर्णेय

🇩🇪 entscheidbar

🇮🇩 dapat diputuskan

🇺🇦 вирішуваний

🇵🇱 rozstrzygalny

🇯🇵 決定可能

🇫🇷 décidable

🇪🇸 decidible

🇹🇷 karar verilebilir

🇰🇷 결정 가능

🇸🇦 قابل للقرار

🇨🇿 rozhodnutelný

🇸🇰 rozhodnuteľný

🇨🇳 可判定

🇸🇮 odločljiv

🇮🇸 ákveðinn

🇰🇿 шешілетін

🇬🇪 გადაწყვეტადი

🇦🇿 qərar verilə bilən

🇲🇽 decidible

Etymology

The term 'decidable' originated in the field of mathematics and computer science. It is closely related to the concept of computability and the work of mathematicians such as Alan Turing and Kurt Gödel. The study of decidability has had a profound impact on the development of algorithms and formal languages.