CYK Algorithm

Definition

The CYK (Cocke-Younger-Kasami) algorithm is a parsing algorithm used for context-free grammars in Chomsky Normal Form. It employs dynamic programming to efficiently determine if a given string can be generated by a specified grammar, making it essential for constituency parsing in Natural Language Processing. The algorithm constructs a parse table that captures possible non-terminal productions for substrings of the input, allowing for systematic checking of whether the entire input string can be produced by the grammar.

5 Must Know Facts For Your Next Test

1. The CYK algorithm operates on grammars that are in Chomsky Normal Form, which means all productions must conform to specific formats to work properly.
2. It uses a triangular parse table, where the entry at position (i, j) represents all non-terminals that can generate the substring from position i to j in the input string.
3. The time complexity of the CYK algorithm is O(n^3 * |G|), where n is the length of the input string and |G| is the number of grammar rules, making it efficient for moderate-sized inputs.
4. The algorithm starts by initializing the table with single-character productions and progressively fills in larger substrings by combining results from smaller substrings.
5. If the start symbol of the grammar appears in the table entry for the entire string, then the string can be generated by that grammar.

Review Questions

• How does the CYK algorithm utilize dynamic programming to check if a string can be generated by a context-free grammar?
  • The CYK algorithm employs dynamic programming by constructing a parse table that systematically stores results for substrings of increasing length. It initializes the table with productions for single characters and then combines these results for longer substrings based on grammar rules. This approach minimizes redundant computations and efficiently determines whether the entire input string can be derived from the grammar.
• What are the steps involved in implementing the CYK algorithm on an input string, and how do these steps relate to Chomsky Normal Form?
  • Implementing the CYK algorithm involves several key steps: first, convert the given context-free grammar into Chomsky Normal Form. Then, initialize a triangular parse table based on the input string's length. Fill in this table by checking each substring against non-terminal productions according to the rules of Chomsky Normal Form. Finally, check if the start symbol appears in the parse table entry for the entire input, indicating whether it can be generated by that grammar.
• Evaluate how changes in input length or complexity impact the performance of the CYK algorithm and its practical applications in parsing.
  • As input length increases, the performance of the CYK algorithm becomes significantly impacted due to its cubic time complexity, O(n^3 * |G|). This makes it feasible for shorter strings or simpler grammars but can lead to performance issues with longer or more complex inputs. In practical applications like natural language processing or syntax analysis, this means careful consideration must be given to grammar design and input size to maintain efficiency while using this parsing method.

Related terms

Chomsky Normal Form: A type of context-free grammar where every production rule is in the format of A → BC or A → a, ensuring that each rule produces either two non-terminals or a single terminal.

Dynamic Programming: An optimization technique that solves complex problems by breaking them down into simpler subproblems, storing the results of these subproblems to avoid redundant calculations.

Parse Tree:

A tree structure that represents the syntactic structure of a string according to a given grammar, showing how the string can be derived from the grammar's production rules.