The Early parser by dfhdhdhdhjr


									The Earley parser

    Hadier Azhatiguli
    Plamena Drageva

    21 Janurary 2008

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

     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
Earley item:

   Is an item with an indication of the
    position of the symbol at which the
    recognition of the recognized part
   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
           ,the set contains newly predicted
    items which have a dot in front.
             the set contains active and
    predicted sets.

     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

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

     This reduction goes as follows:
    For each item of the form
    the Completer goes to           ,and calls the
  . 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 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

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

  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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