Decidability: meaning, definitions and examples

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.

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.

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.

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.

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.

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.

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.

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.