A grammar is a mathematical system that generates a language. In order to define a language from a mathematical point of view, one begins with an alphabet A which is simply a set of symbols, either finite or infinite. Let A^* be the set of all sequences of symbols of any length drawn from the alphabet A. A language L over the alphabet A is defined to be some particular subset of A^*. Elements of the language are called sentences. For example if the alphabet A is the set of english words, then A^* is the set of all sequences of english words, and the english language could be defined to be the subset of all such sequences that are grammatically correct english sentences. In general given a language L which is a proper subset of A^*, a grammar G specifies how to produce all elements of L...