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?