1 (40 points) Convert following problems into languages. Use the notation (x) as a string representation of an object r. For example, the problem of determining whether square root of a natural number is a natural number (as discussed in class) can be described n | n is a natural number and Vn is a natural number} a. The problem of determining whether a string has length less than 128. Note that as Is| denotes the length of a string s. b. The problem of determining whether a DFA accepts at least one string c. The problem of determining whether a DFA accepts the empty string. In other words, the language of a DFA is EU L for a language L d. The problem of determining whether the language of an NFA is not empty e. The problem of determining whether a regular expression does not generate a specific string f. The problem of determining whether a Turing machine loops indefinitely g. The problem of determining whether two Turing machines recognize the same language h. The problem of determining whether two deciders produce the same output on their tape (after they halt in their accept state) for a given input string. Note that a decider is a Turing machine that always halt