THE CYK PARSING METHOD (2)

Cornelia Kempa

Carla Parra Escartín

WS 2006-2007

Tübingen, 4th December 2006 2

AGENDA

1. Building the recognition table2. Undoing the effect of the CNF transformation

2.1. Overview2.2. Adding removed elements2.3. Parsing

2.3.1. Methodology2.3.2. Left-most derivation

3. A short retrospective of CYK4. Chart Parsing

Tübingen, 4th December 2006 3

AGENDA

1. Building the recognition table2. Undoing the effect of the CNF transformation

2.1. Overview2.2. Adding removed elements2.3. Parsing

2.3.1. Methodology2.3.2. Left-most derivation

3. A short retrospective of CYK4. Chart Parsing

Tübingen, 4th December 2006 4

2. Undoing the effect of the CNF transformation

2.1. Overview (1)

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2. Undoing the effect of the CNF transformation

2.1. Overview (2)

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2. Undoing the effect of the CNF transformation

2.1. Overview (3)

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AGENDA

1. Building the recognition table2. Undoing the effect of the CNF transformation

2.1. Overview

2.2. Adding removed elements2.3. Parsing

2.3.1. Methodology2.3.2. Left-most derivation

3. A short retrospective of CYK4. Chart Parsing

Tübingen, 4th December 2006 8

2.2. Adding removed elements (1)

2. Undoing the effect of the CNF transformation

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CYK does not require all non-terminals reachable.

Rule added!!!

+

2.2. Adding removed elements (2)

2. Undoing the effect of the CNF transformation

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New line

2. Undoing the effect of the CNF transformation

2.2. Adding removed elements (3)

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Set Rsi, 0

non-terminals that can be considered as possibly occurring just in front of symbol zi

Set Rsn +1,0

non-terminals that can occur at the end of the sentence.

2.2. Adding removed elements (4)

2. Undoing the effect of the CNF transformation

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AGENDA

1. Building the recognition table2. Undoing the effect of the CNF transformation

2.1. Overview2.2. Adding removed elements

2.3. Parsing2.3.1. Methodology2.3.2. Left-most derivation

3. A short retrospective of CYK4. Chart Parsing

Tübingen, 4th December 2006 13

Derivation starts with start-symbol S.Is A1A2···Am a right hand side of S?

Does A1A2···Am derive S1,n?

We check this starting with A1

2 cases:

2. Undoing the effect of the CNF transformation2.3. Parsing

2.3.1. Methodology (1)

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A) A1 is a terminal symbol

it must be the first symbol of s1,n

then check if A2···Am derives s2,n-1

B) A1 is a non-terminal symbol

it must be a member of Rs1,k

then check if A2···Am derives s2,k+1,n-k

2. Undoing the effect of the CNF transformation2.3. Parsing

2.3.1. Methodology (2)

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Now: determined whether the rule is applicable

if so, which parts of the rule derive which substrings.

Next step: determine how the substrings can be derived.

2. Undoing the effect of the CNF transformation2.3. Parsing

2.3.1. Methodology (3)

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AGENDA

1. Building the recognition table2. Undoing the effect of the CNF transformation

2.1. Overview2.2. Adding removed elements2.3. Parsing

2.3.1. Methodology

2.3.2. Left-most derivation

3. A short retrospective of CYK4. Chart Parsing

Tübingen, 4th December 2006 17

2. Undoing the effect of the CNF transformation2.3. Parsing

2.3.2. Left-most derivation (1)

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2. Undoing the effect of the CNF transformation2.3. Parsing

2.3.2. Left-most derivation (2)

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This is what we saw so far:

If we continue... The derivation is:

2. Undoing the effect of the CNF transformation2.3. Parsing

2.3.2. Left-most derivation (3)

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2. Undoing the effect of the CNF transformation2.3. Parsing

2.3.2. Left-most derivation (4)

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AGENDA

1. Building the recognition table2. Undoing the effect of the CNF transformation

2.1. Overview2.2. Adding removed elements2.3. Parsing

2.3.1. Methodology2.3.2. Left-most derivation

3. A short retrospective of CYK4. Chart Parsing

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First: recognition table using the original grammar.

Then: transforming grammar to CNF.

3. A short retrospective of CYK (1)

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For efficiency, CNF is a bit too restrictive

Disadvantage of CNF: • Resulting recognition table lacks the

information we need to construct a derivation using the original grammar!

3. A short retrospective of CYK (2)

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In the transformation process, some non-terminals were thrown away

(non-productive)Missing information could be added.

3. A short retrospective of CYK (3)

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Result: almost the same recognition table.• Extra information on non-terminals

• Obtained in a simpler and much more efficient way.

3. A short retrospective of CYK (2)

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AGENDA

1. Building the recognition table2. Undoing the effect of the CNF transformation

2.1. Overview2.2. Adding removed elements2.3. Parsing

2.3.1. Methodology2.3.2. Left-most derivation

3. A short retrospective of CYK

4. Chart Parsing

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CYK algorithm also known as chart parsing.

Both techniques variants

(some of them identical among the techniques)

Difference: implementation.

4. Chart parsing (1)

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A chart is just a recognition table.

4. Chart parsing (2)

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FINAL OVERVIEW (1)

1. Building the recognition table

2. Possible Derivations

3. Undoing the effect of the CNF transformation.

4. A short retrospective of CYK

5. Chart Parsing

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PARSING METHODS

Non-directional methods

Top-down Bottom-up

Unger Parser CYK Parser

FINAL OVERVIEW (2)

THANK YOU VERY MUCH