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Problem 1: Parse Trees. Assume that in the sentence “Father made her fish.” the word “her” can be either a personal (PRP) or possessive pronoun (PRP$), and the word “fish” can be either a noun (NN) or a verb (VB). Draw the two possible parse trees for this sentence corresponding to the interpretations of “Father prepared a meal with the fish she owned” versus “Father got her to catch a fish.” Drawing rules from the book, list all the rules needed to draw these parses, adding rules as needed, including those transforming parts of speech to words.
Problem 2: Chomsky Normal Form. Convert your grammar from problem 1 to Chomsky Normal Form.
Problem 3: CKY Parsing. Write out the complete CKY parse table for the sentence "Father made her fish" using your grammar from Problem 2. Make sure to include the pointers that indicate the backtraces, as shown at the bottom of Figure 13.12. How many possible parses are there?
Problem 4: Earley Parsing. Write out the complete Earley chart for the sentence "Father made her fish" using your grammar from Problem 1. Draw arrows between states (analogous to those in the CKY chart) that indicate how the parse trees should be constructed.
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