CockeYoungerKasami

Cocke-Younger-Kasami (CYK) is a parsing algorithm used in computer science to determine whether a given string can be generated by a given context-free grammar. It is named after its inventors, Thomas Cocke, Daniel Younger, and Stephen Kasami, who independently developed the algorithm in the early 1960s. The CYK algorithm is particularly useful for parsing natural languages and programming languages, as well as for other applications where context-free grammars are employed.

The algorithm works by constructing a parse table for the input string, where each cell in the table represents a substring of the input and contains a set of non-terminal symbols that can generate that substring. The table is filled in a bottom-up manner, starting with the smallest substrings and working up to the entire input string. If the start symbol of the grammar is in the top-right cell of the table, then the input string is accepted as valid; otherwise, it is rejected.

The CYK algorithm has a time complexity of O(n^3), where n is the length of the input string. This makes it less efficient than some other parsing algorithms, such as the Earley algorithm, which has a time complexity of O(n^2) for certain types of grammars. However, the CYK algorithm is still widely used due to its simplicity and ease of implementation.

In summary, the Cocke-Younger-Kasami algorithm is a fundamental parsing technique in computer science, enabling the determination of whether a string can be generated by a context-free grammar. Its bottom-up approach and time complexity make it a valuable tool for various applications in natural language processing and programming language analysis.