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The CYK Algorithm
David Rodriguez-VelazquezCS
–
6800Summer I -2009
The CYK Algorithm
ã
The membership problem
:
–
Problem:
ã
Given a context-free grammar
G
and a string
w
–
G
= (V,
∑
,P , S) where
»
V finite set of variables
»
∑ (the alphabet) finite set of terminal symbols
»
P finite set of rules
»
S start symbol (distinguished element of V)
»
V and ∑ are assumed to be disjoint
–
G
is used to generate the string of a language
–
Question:
ã
Is
w
in
L
(
G
)?
The CYK Algorithm
ã
J. Cocke
ã
D. Younger,
ã
T. Kasami
–
Independently developed an algorithm to answer this question.
The CYK Algorithm Basics
–
The Structure of the rules in a Chomsky Normal Form grammar
–
Uses a “dynamic programming” or “table
-filling
algorithm”

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