The Early parser by dfhdhdhdhjr

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The Earley parser

Plamena Drageva

21 Janurary 2008
Overview

 The Earley parser without look ahead.
 Ambiguous sentences.
 Handling epsilon rules.
BOTTOM-UP PARSING

   Earley parser can be described as
bottom-up recognition.

   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.
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.
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:
The construction of an item set:

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

   Completer inspects the completed
set,which contains the items that have
just been recognized and can now be
reduced.
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.
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
to the set predicted.
   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.
Example:

 Input symbol a-a+a
 Grammar
Constructing a parser tree:
Constructing a parser tree:
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.

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