Decidable - Definition, Meaning, and Examples in English

Definition

^{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.

Interesting Facts

Mathematics

In mathematics, a problem that is decidable means there is a method to find out if the answer is yes or no.
An example of a decidable problem is asking if a number is even or odd.
Several famous theorems discuss which problems can be classified as decidable or undecidable in logic.

Computer Science

In computer science, some algorithms can determine if something is decidable, which is very important in programming.
The Halting Problem is a famous undecidable problem, showing that not all questions have a clear yes or no answer.
Decidable languages are sets where you can create a computer program to determine membership with certainty.

Logic

In formal logic, decidable theories are those for which there is an algorithm that can decide any statement's truth.
An example is propositional logic, where logical statements can be definitively analyzed as true or false.
Some logical systems have undecidable statements, meaning there is no way to resolve them to true or false.

Philosophy

Philosophers sometimes discuss decidable statements when examining what can or cannot be known in a logical context.
The distinction between decidable and undecidable issues raises questions about the limits of human knowledge.
Not every philosophical question is decidable, leading to debates that may have no clear resolution.

Game Theory

In game theory, some strategy problems can be decidable, allowing players to determine optimal moves.
Games like chess are often analyzed for decidable strategies, though the full complexity of the game can lead to undecidability.
Decidable strategies help players understand win/loss conditions in competitive scenarios.

Origin of 'decidable'

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.

Decidable Meaning: Definition, Examples, and Translations