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)
Tübingen, 4th December 2006 7
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
Tübingen, 4th December 2006 9
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
Tübingen, 4th December 2006 12
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)
Tübingen, 4th December 2006 15
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)
Tübingen, 4th December 2006 21
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 22
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
Tübingen, 4th December 2006 30
PARSING METHODS
Non-directional methods
Top-down Bottom-up
Unger Parser CYK Parser
FINAL OVERVIEW (2)
THANK YOU VERY MUCH
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