The CKY algorithm requires grammars to first be in CNF.
Grammars in CNF are restricted to rules of the form A -> B C or A -> w.
The right hand-side of each rule must expand either to two non-terminals or to a single terminal.

Situation 1 : mix terminals with non-terminals on the right-hand side

Situation 2 : single non-terminal on the right-hand side (unit productions).

Situation 3 : the length of the right-hand side is greater than 2


Conversion to Chomsky Normal Form

CKY Recognition

State University of New York at Stony Brook

Structural ambiguity occurs when the grammar can assign more than one parse
to a sentence. Two common kinds of ambiguity are attachment ambiguity and coordination ambiguity. A sentence has an attachment ambiguity if a particular constituent can be attached to the parse tree at more than one place. For instance, in the following example the gerundive-VP flying to Paris can be part of a gerundive sentence whose subject is the Eiffel Tower or it can be an adjunct modifying the VP headed by saw:
We saw the Eiffel Tower flying to Paris.
In coordination ambiguity phrases can be conjoined by a conjunction like and. For example, the phrase old men and women can be bracketed as [old [men and women]], referring to old men and old women, or as [old men] and [women], in
which case it is only the men who are old.
The fact that there are many grammatically correct but semantically unreasonable parses for naturally occurring sentences is an irksome problem that affects all parsers. Fortunately, the CKY algorithm is designed to efficiently handle structural ambiguities.

Ambiguity 

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

Speech and Language Processing (3rd ed. draft) 

CKY Parsing

One of the earliest recognition and parsing algorithms.
It is data-driven, bottom-up approach and it's a dynamic programming algorithm.
Standard version can only recognize CFGs in Chomsky Normal Form (CNF).

CKY Algorithm

To resolve disambiguation, the PCFG will calculate a probability of each parse tree (derivation) $T$ of a given sentence $S$. 

The probability of tree $T$ given $S$ is defined as:

$P(T,S) = \prod_{i=1}^{n} P(RHS_i | LHS_i)$

From there, the PCFG will choose the parse tree with the greatest probability as the correct parse of $S$.

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