Prerequisite – Converting Context Free Grammar to Chomsky Normal Form
CYK algorithm is a parsing algorithm for context free grammar.
In order to apply CYK algorithm to a grammar, it must be in Chomsky Normal Form. It uses a dynamic programming algorithm to tell whether a string is in the language of a grammar.
Algorithm :
Let w be the n length string to be parsed. And G represent the set of rules in our grammar with start state S.
 Construct a table DP for size n × n.
 If w = e (empty string) and S > e is a rule in G then we accept the string else we reject.

For i = 1 to n: For each variable A: We check if A > b is a rule and b = w_{i }for some i: If so, we place A in cell (i, i) of our table.

For l = 2 to n: For i = 1 to nl+1: j = i+l1 For k = i to j1: For each rule A > BC: We check if (i, k) cell contains B and (k + 1, j) cell contains C: If so, we put A in cell (i, j) of our table.

We check if S is in (1, n): If so, we accept the string Else, we reject.
Example –
Let our grammar G be:
S > AB  BC A > BA  a B > CC  b C > AB  a
We check if baaba is in L(G):
 We first insert single length rules into our table.
 We then fill the remaining cells of our table.
 We observe that S is in the cell (1, 5), Hence, the string baaba belongs to L(G).
Time and Space Complexity :
 Time Complexity –
O(n^{3}.G)
Where G is the number of rules in the given grammar.
 Space Complexity –
O(n^{2})
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Recommended Posts:
 Regular Expressions, Regular Grammar and Regular Languages
 Closure Properties of Context Free Languages
 Ambiguity in Context free Grammar and Context free Languages
 Simplifying Context Free Grammars
 Ambiguity in Context free Grammar and Context free Languages
 Contextsensitive Grammar (CSG) and Language (CSL)
 Converting Context Free Grammar to Chomsky Normal Form
 Relationship between grammar and language in Theory of Computation
 Converting Context Free Grammar to Greibach Normal Form
 Hypothesis (language regularity) and algorithm (Lgraph to NFA) in TOC
 Check if the language is Context Free or Not
 Regular Expression Vs Context Free Grammar
 Removing Direct and Indirect Left Recursion in a Grammar
 Various Properties of context free languages (CFL)
 Difference between Ambiguous and Unambiguous Grammar
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