Dene a ZPP-machine to be a probabilistic Turing machine

Chapter , Problem 10.20

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Dene a ZPP-machine to be a probabilistic Turing machine that is permitted three types of output on each of its branches: accept, reject, and ?. A ZPP-machine M decides a language A if M outputs the correct answer on every input string w (accept if w A and reject if w 6 A) with probability at least 2 3, and M never outputs the wrong answer. On every input, M may output ? with probability at most 1 3. Furthermore, the average running time over all branches of M on w must be bounded by a polynomial in the length of w. Show that RP coRP = ZPP, where ZPP is the collection of languages that are recognized by ZPP-machines.

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