computability
Noun
- The property of being computable: "computability" refers to the quality or state of a problem, function, or set being solvable or calculable by an effective algorithm or mechanical procedure. It is a fundamental concept in computer science and mathematical logic, particularly in the theory of computation.
- (The property of being solvable algorithmically.)
- (The study of what problems are algorithmically solvable.)
"computability theory": a branch of theoretical computer science and mathematics that studies which problems can be solved by algorithms and the inherent limitations of computation.
- Computability theory explores questions like the halting problem, which is a classic example of non-computability. (The field that investigates algorithmic solvability.)
"degree of computability": a measure of how difficult a problem is to solve algorithmically, often studied in recursion theory.
- Different problems have different degrees of computability, ranging from easily solvable to undecidable. (Levels of algorithmic solvability.)
Computable (adj): capable of being computed or solved by an algorithm.
- This function is computable by a simple program. (It can be calculated algorithmically.)
Non-computability (n): the property of not being computable.
- The halting problem demonstrates the existence of non-computability in mathematics. (The state of being unsolvable algorithmically.)
- Decidability: the property of a problem having a yes-or-no answer that can be determined algorithmically (often used interchangeably in logic).
- Solvability: the ability to be solved or calculated by a method.
Beyond computability: referring to problems that cannot be solved by any algorithm, no matter how powerful the computer.
- Some mathematical truths are beyond computability, meaning no machine can prove them. (Outside the scope of algorithmic solution.)
Limits of computability: the boundaries of what can be computed.
- Understanding the limits of computability helps us know which problems are worth trying to solve with computers. (The frontier of algorithmic solvability.)