The importance of the CYK algorithm stems from the fact that it constructively proves that the [[membership problem]] for context-free languages is [[decision problem|decidable]] (see also: [[theory of computation]]) and the fact that it does so quite efficiently.
TheUsing [[Landau symbol]]s, the worst case [[asymptotic]] time complexity of CYK is [[Big<math>\Theta(n^3 O\cdot notation|Θ]](n<sup>3G|)</supmath>), where ''n'' is the length of the parsed string and ''|G|'' is the size of the CNF grammar ''G''. This makes it one of the most efficient (in those terms) algorithms for recognizing general context-free languages. Specialized and faster algorithms exist for certain subsets of the context-free languages.
