The Earley parser

1
The Earley parser

• Hadier Azhatiguli
• Plamena Drageva
• 21 Janurary 2008

2
Overview

• The Earley parser without look ahead.
• Ambiguous sentences.
• Handling epsilon rules.
• The prediction look ahead.
• The reduction look ahead.

3
TOP-DOWN RESTRICTED BREADTH-FIRST
BOTTOM-UP PARSING

• Earley parser can be described as breadth-first
  top-down parser with bottom-up recognition.

4
Earley parser without look-ahead

• Earley sets
• . We have a set of partial solutions which is
  modified by each symbol we read.we shall write
  the sets between input symbols as we go.
• .The set consists items.

5
Items in the set

• It is grammar rule with a gap in its right hand
  side.
• The gap is traditionally shown as a fat dot.

6
Earley item

• Is an item with an indication of the position of
  the symbol at which the recognition of the
  recognized part started.
• We shall write after the item.
• Example

7
The construction of an item set

• The construction of item set proceeds in three
  phases
• Scanner.
• Completer.
• Predictor.

8
The construction of an item set

• .The Scanner ,Completer and Predictor deal with
  four sets of items for each token.
• .Input symbol at position p is surrounded by
  four sets
• ,which contains items
  avaliable just before
• ,the set contains items which
  have a dot at the end.

9
Construction of an item set

• that contains the non-completed items
  which have a dot in the middle or front
• ,the set contains newly predicted
  items which have a dot in front.
• the set contains active and
  predicted sets.

10
Scanner

• The scanner looks at ,goes through
• and makes copies all of the items
  that contains . .Consequently ,the scanner
  changes into .if dot is at the end
  ,it stors the item in the completed set
  ,otherwise in the active set.

11
Completer

• Completer inspects the completed set,which
  contains the items that have just been
  recognized and can now be reduced.

12
Reduction

• This reduction goes as follows
• For each item of the form
• the Completer goes to ,and calls
  the Scanner.
• . Scanner will make copies all of the items
• in featuring a ,
  replacing
• the by and store them in either
  completed set or active set.

13
Predictor

• Predictor goes through active and predicted
  sets(which is empity initially)
• ,and considers all non-terminals which have a
  dot in front of them.
• .For each predicted non-terminal N and for each
  rule for that non-terminal N?P
• the predictor adds an item
• to the set predicted.

14

• If the completed set for the last symbol in the
  input contains an item
• ,an item spanning the
• whole input and reducing to the start
  symbol,we have found at least one parsing.

15
Example

• Input symbol a-aa
• Grammar

16
(No Transcript)
17
Constructing a parser tree
18
Constructing a parser tree
19
Tabulation

• In The table
• . Columns indicate the begining of possibily
  recognized fragments,all items with the same
• come in the same column.
• . Completed items are drawn in the top left
  corner of a box,active items in bottom right
  corner.Predicted items live in the bottom layer.

20
(No Transcript)