CYK Parsing

This is a Method page for CYK Parsing.

The Cocke–Younger–Kasami (CYK) algorithm is an algorithm for parsing PCFG. It is bottom up and makes use of dynamic programming.

Description

The input to the algorithm is a grammar $G$ in Chomsky Normal Form, and a sentence $X$. The idea behind the parsing algorithm is to recursively build parses from bottom up, and mantaining a chart C[i, j] which contains productions that generates X[i] ... X[j].

Pseudocode

for each i = 1 to n
  for each production A -> a
    if a == X[i]
      add (A -> a, 0) to C[i,i]

for each L = 2 to n
  for each i = 1 to n-L+1
    for each j = 1 to L - 1
      for each production A -> A1 A2
        if A1 in C[i,i+j] and A2 in C[i+j+1,i+L]
          add (A -> A1 A2, i+j) to C[i,i+L]

We can recover the parse trees by traversing through the chart, which contains the production rule used and the point where the subtrees are split. The probability of a parse tree is simply the product of the probability of each production rule that we have used.

References

CKY parsing was briefly covered in Class_Meeting_for_10-710_10-11-2011