(Derived from Barton et al. (1987)) This exercise concerns a language we call Buffalo ⁿ, which is very much like English (or at least E₀) except that the only word in its lexicon is buffalo. Here are two sentences from the language:

Buffalo buffalo buffalo Buffalo buffalo.

Buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo.

In case you don’t believe these are sentences, here are two English sentences with corresponding syntactic structure:

Dallas cattle bewilder Denver cattle.

Chefs London critics admire cook French food.

Write a grammar for Buffalo ⁿ. The lexical categories are city, plural noun, and (transitive) verb, and there should be one grammar rule for sentence, one for verb phrase, and three for noun phrase: plural noun, noun phrase preceded by a city as a modifier, and noun phrase followed by a reduced relative clause. A reduced relative clause is a clause that is missing the relative pronoun. In addition, the clause consists of a subject noun phrase followed by a verb without an object an example reduced relative clause is “London critics admire” in the example above. Tabulate the number of possible parses for Buffalo ⁿ for n up to 10. Extra credit: Carl de Marcken calculated that there are 121,030,872,213,055,159,681,184,485 Buffalo ⁿ sentences of length 200 (for the grammar he used). How did he do that?