Question: (1) (15 = 8 + 7 points) Define a useful state in a Turing Machine M to be such that it is entered by

(1) (15 = 8 + 7 points) Define a useful state in a Turing Machine M to be such that it is entered by M during computation on some input string. We define corresponding language USEFUL-STATE as follows: The language USEFUL-STATE consists of bit strings of the form x#q, such that the Turing machine M enters state q on some input y during its computation. X (a) Is USEFUL-STATE semidecidable? (b) Is USEFUL-STATE decidable?

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