The standard version of CYK can only recognize languages defined by context-free grammars in Chomsky Normal Form (CNF). However, since any context-free grammar can be converted to CNF without too much difficulty, CYK can be used to recognize any context-free language. It is also possible to extend the CYK algorithm to handle some grammars which are not in CNF, although at the cost of making the algorithm significantly harder to understand.

The worst case asymptotic time complexity of CYK is &Theta(n^{3}), where *n* is the length of the parsed string. This makes it the most efficient (in those terms) algorithm for recognizing a context-free language. However, in many cases, other algorithms will give better performance.

The CYK algorithm is important theoretically, since it can be used to constructively prove that the membership problem for context-free languages is decidable.

The CYK algorithm for the membership problem is as follows:

- Let the input string be a sequence of
*n*letters*a*_{1}...*a*_{n}. - Let the grammar contain
*r*terminal and nonterminal symbols*R*_{1}...*R*_{r}, and let R_{1}be the start symbol. - Let P[n,n,r] be an array of booleans. Initialize all elements of P to false.
- For each i = 1 to n
- For each unit production R
_{j}-> a_{i}, set P[i,1,j] = true.

- For each unit production R
- For each i = 2 to n -- Length of span
- For each j = 1 to n-i+1 -- Start of span
- For each k = 1 to i-1 -- Partition of span
- For each production R
_{A}-> R_{B}R_{C}- If P[j,k,B] and P[j+k,i-k,C] then set P[j,i,A] = true

- For each production R

- For each k = 1 to i-1 -- Partition of span

- For each j = 1 to n-i+1 -- Start of span
- If P[1,n,1] is true
- Then string is member of language
- Else string is not member of language

It is simple to extend the above algorithm to not only determine if a sentence is in a language, but to also construct a parse tree, by storing parse tree nodes as elements of the array, instead of booleans. Since the grammars being recognized can be ambiguous, it is necessary to store a list of nodes (unless one wishes to only pick one possible parse tree); the end result is then a forest of possible parse trees.

It is also possible to extend the CYK algorithm to parse Stochastic context-free grammars (SCFGs).