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).

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

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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