Decidability Meaning: Definition, Examples, and Translations

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decidability

[dɪˌsaɪdəˈbɪləti ]

Definitions

^{Context #1 | Noun}

theory

The property of a decision problem that can be solved by an algorithm.

Synonyms

computability, determinability, solubility.

Which Synonym Should You Choose?

Word	Description / Examples
decidability	Used in mathematical logic and computer science to describe whether a problem can be resolved by an algorithm. It refers to problems that have a clear yes or no answer. Decidability is an important concept in understanding which problems can be solved by computational methods. The problem of whether a given algorithm will halt on all inputs is an example of decidability.
computability	Refers to whether a problem or function can be solved or computed by an algorithm. This term is more general than 'decidability' and is used extensively in theoretical computer science. The Church-Turing thesis explores the limits of computability and its implications. Computability helps us understand which functions can be effectively computed by machines.
solubility	Primarily used in chemistry to refer to the ability of a substance to dissolve in a solvent. Can also be used more broadly to discuss the ability to solve a problem. The solubility of salt in water is a basic concept in chemistry. We are assessing the solubility of this new compound in various solvents.
determinability	Refers to the ability to determine a specific outcome in various contexts such as mathematics, physics, or everyday decisions. Less commonly used compared to the other terms. The determinability of the system's behavior under different conditions was key to our experiment. While solving the equation, we evaluated the determinability of each variable.

Examples of usage

The decidability of the halting problem is a fundamental concept in computer science.
Mathematical logic deals with questions of decidability and undecidability.

^{Context #2 | Noun}

philosophy

The ability to make a decision or determine a course of action.

Synonyms

conclusiveness, determination, resolution.

Which Synonym Should You Choose?

Word	Description / Examples
decidability	Used mostly in theoretical and technical contexts, such as mathematics and computer science, to describe whether a problem or question can be definitively solved. The decidability of the algorithm was proven by the researchers. He focused on the decidability of logical theories in his thesis.
determination	Commonly used to describe a strong will or firmness in making decisions or achieving goals. Can also refer to the process of making a decision. Her determination to succeed was evident in her relentless work ethic. The determination of the winner took longer than expected.
resolution	Used to describe the act of solving a problem or the firmness of a decision. Also commonly used during discussions about New Year's resolutions. The resolution of the conflict required weeks of negotiation. She made a resolution to exercise more this year.
conclusiveness	Appropriate when describing evidence or an argument that definitively proves a point without room for doubt. The DNA evidence provided conclusiveness in the court case. Her argument had such conclusiveness that no one could rebut it.

Examples of usage

Decidability is crucial in ethical dilemmas.
The lack of decidability in the situation led to confusion.

Translations

To see the translation, please select a language from the options available.

Interesting Facts

Mathematics

Decidability is often discussed in relation to problems in logic and mathematics, where some problems can be definitively answered while others cannot.
An example of an undecidable problem is the Halting Problem, which asks whether a computer program will stop running or continue forever.
In mathematical logic, more complex systems often lead to undecidable statements, meaning they cannot be proved or disproved within those systems.

Computer Science

The concept plays a crucial role in theoretical computer science, particularly in understanding the limits of computation and what can be algorithmically resolved.
In programming, a decidable problem can often be solved by an algorithm, while undecidable problems require more complex reasoning or heuristic approaches.
Tools like model checkers rely on the concept of decidability to verify whether systems behave correctly, giving practical applications in software engineering.

Philosophy

Philosophers ponder the implications of decidability when it comes to morality, ethics, and other philosophical inquiries where clear answers may be elusive.
The limits of decidability raise questions about human cognition and the boundaries of knowledge, as some issues may never be definitively resolved.
The concept challenges the idea that all questions can be answered and illustrates the interplay between knowledge and uncertainty.

Linguistics

In linguistics, decidability can pertain to whether the meaning of sentences can be unambiguously determined.
Some language constructs lead to ambiguities, making it undecidable whether a particular interpretation is correct or not.
The study of decidability in language can shed light on how people comprehend meaning and resolve ambiguity in communication.

Game Theory

In game theory, decidability can refer to whether a strategy for winning a game can be effectively determined.
Some decision problems in games can be classified as determinable or non-determinable, affecting how strategies are developed.
Understanding which games have decidable outcomes helps in creating more complex and interesting game designs.

Origin of 'decidability'

The term 'decidability' originated in the early 20th century in the field of mathematical logic. It was first used in the context of decision problems that could be solved by a mechanical procedure. Over time, the concept of decidability expanded to other disciplines such as computer science, philosophy, and ethics. Today, decidability is a key concept in algorithmic theory and plays a crucial role in various areas of study.