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The Early parser

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					The Earley parser

    Hadier Azhatiguli
    Plamena Drageva

    21 Janurary 2008
Overview

  The Earley parser without look ahead.
  Ambiguous sentences.
  Handling epsilon rules.
  The prediction look ahead.
  The reduction look ahead.
TOP-DOWN RESTRICTED BREADTH-FIRST
      BOTTOM-UP PARSING


     Earley parser can be described as
      breadth-first top-down parser with
      bottom-up recognition.
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.
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
    the predictor adds an item
    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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posted:8/30/2012
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