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## PowerPoint Slideshow about ' Simplifications of Context-Free Grammars' - tyrone-santiago

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### The CYK Parser

COMP 335

COMP 335

COMP 335

COMP 335

useless

Variables

useless

useless

useless

useless

useless

useless

A production is useless

if any of its variables is useless

COMP 335

that produce terminal symbols:

(the rest variables are useless)

Remove useless productions

COMP 335

reachable from S

(the rest variables are useless)

Final Grammar

Remove useless productions

COMP 335

Removing All

- Step 1: Remove -productions
- Step 2: Remove Unit-productions
- Step 3: Remove Useless productions

COMP 335

Introduce intermediate variable:

COMP 335

Introduce intermediate variable:

COMP 335

From any context-free grammar

(which doesn’t produce )

not in Chomsky Normal Form

we can obtain:

An equivalent grammar

in Chomsky Normal Form

COMP 335

For any context-free grammar

(which doesn’t produce )

there is an equivalent grammar

in Chomsky Normal Form

COMP 335

- Chomsky normal forms are good
- for parsing and proving theorems

- It is very easy to find the Chomsky normal
- form for any context-free grammar

COMP 335

For any context-free grammar

(which doesn’t produce )

there is an equivalent grammar

in Greibach Normal Form

COMP 335

- Greibach normal forms are very good
- for parsing

- It is hard to find the Greibach normal
- form of any context-free grammar

COMP 335

COMP 335

Time Complexity:

Observation:

The CYK algorithm can be

easily converted to a parser

(bottom up parser)

COMP 335

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