Ambiguous sentences Characteristics and Problems

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Ambiguous sentencesCharacteristics and Problems

• More than one item can represent the same set
  which leads to ambiguity
• the parse trees will be produced top-down
• when searching a completed set for items of the
  form
• there may be exponentially many parse trees or
  even infinitely many of them

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• while predicting items it may stumble upon an
  empty prediction which means that the
  non-terminal A has been completed just before
  symbol number and this completed item should be
  added to the completed set
• run the Completer again and it will draw the
  consequences of the newly completed items
• if it finds occurrences of the predicted
  non-terminal new predictions have to be done
  which means more work for the Completer

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keep running the predictor and the completer in
turn
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Prediction look-ahead

• In a prediction step the next terminal is used as
  look-ahead and we check whether
• it is a member of the first set of the RHS of
  the production we want to predict and only if it
  si positive we want to make the prediction
• a Predictor that will never predict anything
  obviously erroneous all its predicted items will
  be either completed or active in the next set.(
  The predictions may however fail on the symbol
  after that).

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• The artificial grammar of figure 7.19 produces
  nothing but the three sentences p,q and pq,and
  does so in a straightforward way.The root is S
  rather than S

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Parsing of the sentence q

• Starting from the initial item,the Predictor
  predicts a list of 7 items.
• looking at the next symbol,q,the Predictor
• could easily avoid the prediction C?.p_at_1, but
  several of the other predictions are also false
• the Predictor could avoid the first since it
  sees that it cannot begin with q
• Itemset1 is empty,indicating that there is no waz
  for the input to continue
• calculate the first sets of all non-terminals in
  the grammar

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• the Predictor starts again from the initial item
• predictive look-ahead reduces the number
• of items by 20 to 50 or even more on
  practical grammars

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Reduction look-ahead

• calculate the FIRST sets, we can use them for
  asecond type of look-ahead
• reduction look-ahead reduces the number
• of completed items
• the redunduncy of the completed items
• are only meaningful at the end of the input
• keep,together with any item, a set of symbols
  which may come after that item,the reduction
  look-ahead setif the item seems completed but
  the next symbol is not in this set,the item is
  discarded

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Construction of a look-ahead set

• straightforward rules
• the prediction look-ahead cannot be calculated
  in advance
• a limited and less effective set could be
  calculated statically,using the FOLLOW sets
• the initial item starts with a look-ahead set of
  
• when the dot advances in an item, the look-
  ahead set remains the same
• when a new item is created by the Predictor, a
  new look-ahead set must be composed
• the look-ahead ... Is used to indicate that the
  look-ahead is not yet known but does not
  influence the look-ahead the item contributes

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Suppose that the item is P?A . BCD a b c _at_n

• What symbols may follow the occurrence of B in
  this item
• any symbol C can start with
• if C can produce the empty string ,any symbol D
  can start with
• if D can also produce the empty string, any of
  the symbols a,b and c
• the resulting new reduction look-ahead set is
  written as FIRST(CD abc)

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Effectiveness of prediction look-ahead

• not easily determined
• Earley recommends the reduction look-ahead ,but
  does not take into account the effort required to
  calculate and maintain the look-ahead sets.
• may easily double the number of items to be
  carried around
• Implementation cost and overhead are considerable

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J. Earley, An efficient context-free parsing
algorithm, Commun. ACM, vol. 13, no. 2, p.
94-102, Feb 1970