The difference between a recognizer and a parser is that the latter identifies all possible derivations for given input. Usually, a set of parse trees is produced. If there are many parse trees for average sentences, it becomes an issue how to represent them as compactly as possible. This is done by constructing a parse forest. Parse forest construction will be formulated with the presupposition that a bottom-up recognition algorithm provides the necessary information. We find that the above recursive ascent recognizers do not give enough information. A revised recursive ascent recognizer does the job, however. We also discuss a conventional formulation of the Earley recognizer, and its relation to parse forests.
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