could really use some help with this question on drawing an FSA

Linguists speak of a long distance dependency when the presence/absence or form of something at position i is systematically related to the presence/absence or form of something at position j, and ji can be arbitrarily big. Sometimes people have thought that FSAs cannot encode long distance dependencies. 1. In refutation of this, consider the following FSA which accepts strings over {x,y} of length 2, which must begin and end with the same letter, but otherwise are unconstrained between these positions. In English there are some 'number agreement' requirements concerning the determiner word at the beginning of a noun-phrase and the noun at the end of a noun-phrase, as illustrated by many big cat books many big cat book * each big cat books * each big cat book Intuitively this is an example of a long-distance dependency. Let L1 be a mini-language defined in the following way to encapsulate the essence of this every expression in L1 begins with 'many' or 'each' continues with 0 or more repetitions of 'ADJ (for adjective) ends with a sequence of length 1, beginning with 0 or more repeats of ' N ' (for noun) and ending with books/cats/dogs if the initial word was many book/cat/dog if the initial word was each Give an FSA which defines L1 (HINT: see FSA above). You can sketch this out as a picture. Another possibility would be to put its details into a file of the kind understood by the FSA Utilities program (see 5.6). The latter way would have the advantage of allowing you to possibly test it