State diagram for DFA Mtest 3. (12 points) To safeguard the privacy or security of a network, some software filter the IP addresses that are allowed to send content to computers on the network. The IP address can be broken into parts that represent the source host of incoming traffic, including geographic data. As a result, software needs to be designed to recognize whether certain substrings (representing permitted hosts) are present (if the hosts are permitted to send data) and whether others are absent (if those hosts are blocked from sending data) In this question, you'l design ways to detect these patterns in strings and analyze their costs (a) Over the alphabet 0,1,2,3, 4,5,6,7,8,9 design a NFA that accepts each string with the substring 127 or 172. Your NFA should have no more than 5 states. Briefly justify your construction by explaining the role each state plays in the machine. In the context of network security, this NFA would only allow traffic from with IPs that have prior approval. (b) Alternatively, suppose the network administrators want to block traffic from IP addresses that have been associated with spammers. Over the alphabet 0, 1, 2, 3, 4, 5,6,7,8,9 design a NFA that accepts each string that does not have the substring 127 and does not have the substring 172. Your NFA should have no more than 5 states. Briefly justify your construction by explaining the role each state plays in the machine or by explaining the process of obtaining this machine using the general constructions discussed in class and in the textbook Hint: The set in this part is the complement of the set in part (a) Caution: The construction which flips accept and reject states in a machine to obtain a new machine that recognizes the complement of the language of the original works for DFA the machine here is a NFA. (c) For this part of the question, consider the smaller alphabet -fa, b, c. The language (w E * | w has the substring ab} is described by the regular expression ab Find a regular expression that describes the complement of this set of strings (w * | tu doesn't have the substring ab) Briefly justify why your regular expression works