The CKY algorithm is a fundamental parsing technique in natural language processing. It uses dynamic programming to determine whether a sentence can be generated by a context-free grammar, and constructs parse trees showing the grammatical structure. The algorithm requires the grammar to be in Chomsky Normal Form, where production rules follow specific patterns.
Before applying the CKY algorithm, the grammar must be converted to Chomsky Normal Form. CNF restricts production rules to two specific types: rules that produce two non-terminals, and rules that produce a single terminal symbol. This standardization enables the dynamic programming approach used in CKY parsing.
The CKY algorithm uses a triangular table structure. Each cell represents possible non-terminals that can generate a substring of the input sentence. The bottom row contains the terminal symbols from the sentence, while higher rows represent longer substrings. The algorithm fills the table bottom-up, combining smaller constituents to form larger ones.
The CKY algorithm follows a systematic bottom-up approach. First, we initialize the bottom row with terminal symbols from the grammar. Then, for each cell representing longer substrings, we try all possible ways to split the substring and check if any grammar rules can combine the parts. Valid non-terminals are added to each cell. Finally, we check if the top cell contains the start symbol.
The CKY algorithm has wide applications in natural language processing, including syntax parsing, grammar checking, and machine translation. Its time complexity is O(n³|G|), where n is the sentence length and |G| is the grammar size. While this cubic complexity might seem high, CKY remains efficient for practical applications and serves as a foundation for more advanced parsing techniques.
Before applying the CKY algorithm, the grammar must be converted to Chomsky Normal Form. CNF restricts production rules to two specific types: rules that produce two non-terminals, and rules that produce a single terminal symbol. This standardization enables the dynamic programming approach used in CKY parsing.
The CKY algorithm uses a triangular table structure. Each cell represents possible non-terminals that can generate a substring of the input sentence. The bottom row contains the terminal symbols from the sentence, while higher rows represent longer substrings. The algorithm fills the table bottom-up, combining smaller constituents to form larger ones.
The CKY algorithm follows a systematic bottom-up approach. First, we initialize the bottom row with terminal symbols from the grammar. Then, for each cell representing longer substrings, we try all possible ways to split the substring and check if any grammar rules can combine the parts. Valid non-terminals are added to each cell. Finally, we check if the top cell contains the start symbol.
The CKY algorithm has wide applications in natural language processing, including syntax parsing, grammar checking, and machine translation. Its time complexity is O(n³|G|), where n is the sentence length and |G| is the grammar size. While this cubic complexity might seem high, CKY remains efficient for practical applications and serves as a foundation for more advanced parsing techniques.