Consider the following simple PCFG for noun phrases:
0.6: NP $\rightarrow$ Det\ AdjString\ Noun
0.4: NP $\rightarrow$ Det\ NounNounCompound
0.5: AdjString $\rightarrow$ Adj\ AdjString
0.5: AdjString $\rightarrow$ $\Lambda$
1.0: NounNounCompound $\rightarrow$ Noun
0.8: Det $\rightarrow$ the
0.2: Det $\rightarrow$ a
0.5: Adj $\rightarrow$ small
0.5: Adj $\rightarrow$ green
0.6: Noun $\rightarrow$ village
0.4: Noun $\rightarrow$ green
where $\Lambda$ denotes the empty string.
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What is the longest NP that can be generated by this grammar? (i) three words(ii) four words(iii) infinitely many words
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Which of the following have a nonzero probability of being generated as complete NPs? (i) a small green village(ii) a green green green(iii) a small village green
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What is the probability of generating “the green green”?
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What types of ambiguity are exhibited by the phrase in (c)?
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Given any PCFG and any finite word sequence, is it possible to calculate the probability that the sequence was generated by the PCFG?