Consider the following PCFG for simple verb phrases:
0.1: VP
$\rightarrow$ Verb
0.2: VP
$\rightarrow$ Copula Adjective
0.5: VP
$\rightarrow$ Verb the Noun
0.2: VP
$\rightarrow$ VP Adverb
0.5: Verb
$\rightarrow$ is
0.5: Verb
$\rightarrow$ shoots
0.8: Copula
$\rightarrow$ is
0.2: Copula
$\rightarrow$ seems
0.5: Adjective
$\rightarrow$ unwell
0.5: Adjective
$\rightarrow$ well
0.5: Adverb
$\rightarrow$ well
0.5: Adverb
$\rightarrow$ badly
0.6: Noun
$\rightarrow$ duck
0.4: Noun
$\rightarrow$ well
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Which of the following have a nonzero probability as a VP? (i) shoots the duck well well well(ii) seems the well well(iii) shoots the unwell well badly
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What is the probability of generating “is well well”?
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What types of ambiguity are exhibited by the phrase in (b)?
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Given any PCFG, is it possible to calculate the probability that the PCFG generates a string of exactly 10 words?