Please please do it properly
Question 1 For each of the following two languages L, provide a regular expression that defines L and a DFA that decides L. Justify why a string o belongs to L if and only if o matches the regular expression (is in the language defined by the regular expression) and why it belongs to L if and only if the DFA accepts o. (I don't expect a formal proof here, but I want you to justify why you think that the regular expression and DFA you provide are correct answers.) The language L of all binary strings that contain two ls separated by one or two characters. For example, the strings 01011100 and 00100100001 belong to L because the underlined substrings consist of two ls separated by one or two characters. The string 001100011000 does not belong to L because between every pair of 1s, there are no characters or more than two characters. The language L of all binary strings where every pair of consecutive 1s is immediately preceded by at least two Os. For example, the string 0011010001101 belongs to L because, as the underlined substrings show, each pair of consecutive 1s is preceded by two or more Os. The strings 00101101 and 001100011101 do not belong to this language because both contain a pair of consecutive 1s where the two immediately preceding characters include another 1. Question 1 For each of the following two languages L, provide a regular expression that defines L and a DFA that decides L. Justify why a string o belongs to L if and only if o matches the regular expression (is in the language defined by the regular expression) and why it belongs to L if and only if the DFA accepts o. (I don't expect a formal proof here, but I want you to justify why you think that the regular expression and DFA you provide are correct answers.) The language L of all binary strings that contain two ls separated by one or two characters. For example, the strings 01011100 and 00100100001 belong to L because the underlined substrings consist of two ls separated by one or two characters. The string 001100011000 does not belong to L because between every pair of 1s, there are no characters or more than two characters. The language L of all binary strings where every pair of consecutive 1s is immediately preceded by at least two Os. For example, the string 0011010001101 belongs to L because, as the underlined substrings show, each pair of consecutive 1s is preceded by two or more Os. The strings 00101101 and 001100011101 do not belong to this language because both contain a pair of consecutive 1s where the two immediately preceding characters include another 1
