What does computability mean?
Computability is a noun referring to the property of a problem, question, or function being solvable in principle by a finite, mechanical procedure — that is, by an algorithm running on an idealized computing device. The term anchors one of the great intellectual achievements of the twentieth century: the formalization, through the work of logicians such as Kurt Gödel, Alonzo Church, and especially Alan Turing, of exactly what it means for something to be 'effectively calculable.' Computability also names the field of study built on that foundation, known as computability theory, which classifies problems into those that can be decided by computation and those — like the famous halting problem — that provably cannot, regardless of how powerful a computer might be. Closely tied to but distinct from complexity, which measures how costly solutions are to compute, computability addresses the more fundamental prior question: whether a solution exists at all. It remains central to mathematics, logic, and theoretical computer science, and its ideas quietly underpin every program ever written.
nounThe property of a problem or function of being solvable or computable by an effective procedure, such as an algorithm; in mathematics and computer science, the formal study of which problems can, in principle, be solved by mechanical computation.
- The quality or state of being computable — capable of being determined or calculated by an effective mechanical procedure such as an algorithm.
- (As an uncountable mass term) The branch of mathematical logic and theoretical computer science that studies what can and cannot be computed, often called computability theory.
"Turing's 1936 paper laid the foundations for the modern theory of computability."
"The halting problem's undecidability is one of the most famous negative results in computability."
"Students in the course studied computability before moving on to computational complexity."
Very rare; occasionally appears in technical literature when comparing different formal definitions or degrees of computability, but standard usage treats the word as uncountable.
"Different models of calculation give rise to subtly different computabilities, though they largely coincide in practice."
In 1936, Alan Turing proved that some perfectly well-defined problems can never be solved by any computer — no matter how fast — and computability is the field that explains why.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of computability
Computability derives from the verb compute, which comes from the Latin computare, meaning 'to reckon' or 'to calculate', formed from com- ('together') plus putare ('to think, reckon'). The word entered English via French in the early modern period, with the sense of arithmetical calculation well established by the seventeenth century. The abstract noun computability itself is a twentieth-century formation, coined alongside the rise of mathematical logic and the formal study of effective calculation in the 1930s, when Turing, Church, and others gave rigorous definitions of what can be mechanically computed. Its cognates include computation, computable, and computer, all sharing the same Latin root.
How computability is actually used
A technical term used almost exclusively in mathematics, logic, and theoretical computer science; it is nearly always uncountable. In informal contexts it may sound jargonistic, and writers outside these fields typically prefer plain terms like 'solvable' or 'calculable'.
Easily confused with computability
Computability asks whether a problem can be solved by an algorithm at all, while complexity concerns how much time or memory an algorithm needs to solve it.
Computation is the act or process of calculating something, whereas computability is the property of being calculable in principle.