(Derived from Barton et ul. (1987).) This exerci:;e concerns a language we call Buffalon, which is very much like English (or at least Eo), except that the only word in its lexicon is buflulo. Here are two sentences from the language: Buffalo buffalo buffalo Buffalo buffalo. Buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo. In ease 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 Buffalon . The lexical categories are cilty, 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 Bu#alon for n up to 10. Extra credit: Carl de Marcken calculated that there are 121,030,872,213,055,159,68 1,184,485 Buffalon sentences of length 200 (for the grammar he used). How did he do that?