Let L= {u1,..., Uk} be the set of lower case words in the English dictionary and...

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Let L= {u1,..., Uk} be the set of lower case words in the English dictionary and let U= {v1,..., Vk} be the set of words in the English dictionary with the first letter capitalized. We will define an English word as "correct" if it's in (either lower case or upper case) dictionary. We will define an English sentence as being "correct" if • it is composed of a sequence of 1 or more "correct English words" separated by a single space (use or something like that for a space), or a comma followed by a space, • if there is exactly one period directly and it occurs after the last word, • if the first word is capitalized, • no other word is capitalized. A "correct English paragraph" is a sequence of 1 or more correct English sentences separated by a single space. A "correct English document" is a sequence of 1 or more correct English paragraphs separated by newlines (we can use \n' as the newline). (a) Give a regular expression for the set of "correct English words", "correct English sentences", "correct English paragraphs", and "correct English documents". (b) If you have a bunch of text files on a computer, and you wanted to check whether or not they are "correct English documents", how would you do it? (You don't need to provide an algorithm, just a strategy that you know could be coded and justify why you know it could be coded). Let L= {u1,..., Uk} be the set of lower case words in the English dictionary and let U= {v1,..., Vk} be the set of words in the English dictionary with the first letter capitalized. We will define an English word as "correct" if it's in (either lower case or upper case) dictionary. We will define an English sentence as being "correct" if • it is composed of a sequence of 1 or more "correct English words" separated by a single space (use or something like that for a space), or a comma followed by a space, • if there is exactly one period directly and it occurs after the last word, • if the first word is capitalized, • no other word is capitalized. A "correct English paragraph" is a sequence of 1 or more correct English sentences separated by a single space. A "correct English document" is a sequence of 1 or more correct English paragraphs separated by newlines (we can use \n' as the newline). (a) Give a regular expression for the set of "correct English words", "correct English sentences", "correct English paragraphs", and "correct English documents". (b) If you have a bunch of text files on a computer, and you wanted to check whether or not they are "correct English documents", how would you do it? (You don't need to provide an algorithm, just a strategy that you know could be coded and justify why you know it could be coded).

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