Week4-4Earley Parser

Background

• Developed by Jay Earley in 1970
• No need to convert grammar to CNF
• Left to right

Complexity

fast than O(n3) in many cases

Earley Parser

• look for both full and partial constituents
• when reading word k, it has already identified all hypotheses that are consistent with words 1 to k-1

Data structure

• It uses dynamic programming table, just like CKY
• Example entry in column 1:
  
  • [0:1] VP -> VP . PP
  • created when processing word 1
  • corresponds to words 0 to 1 (the part on the left of . represents the part that we have found, thus VP, and if we found later PP, we will find the whole non terminal)
  • the dot(.) separates the completed(known) part from the incomplete(possibly unattainable) part

3 types of entries

• ‘scan’- for words
• ‘predict’ - for non-terminals
• ‘complete’ - otherwise

Example

Take this book.

at the end we could find that it is either a verb phrase or a sentence.

The problem of CFG

Agreement

• Number
  
  • Chen is/ People are
• Person
  
  • I am/ Chen is
• was/ is/ will be
• Case
• Gender

Combinatorial explosion

• Many combinations of rules are needed to express agreement
  
  • S -> NP VP
  • S -> 1sgNP 1sgVP
  • S -> 2sgNP 2sgVP
  • …

Subcategorization frames

For different type of words, the rules we have are different.

• direct object
• prepositional phrase
• predictive adjective
• bare infinitive
• to-infinitive
• participial phrase
• that-clause
• question-form clause

CFG independence assumption

The probability of different non terminals are not independent in the context of rules.

Remark: The solution of it is the Lexicalized CFG(PCFG).

Conclusion

Because the possibilities of combinations, the number of the parses of a sentence is exponential, so to find all the parses, the you have to spend exponential time.