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06s - MCS-265 David Wolfe Homework set 6 solution Due...

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MCS-265 Homework set 6 solution April 14, 2004 David Wolfe Due: April 21, 2004 1. (Warm-up) (Sipser 3.11) A Turing machine with doubly infinite tape is similar to an ordinary Turing machine except that its tape is infinite to the left as well as to the right. The tape is initially filled with blanks except for the portion that contains the input. Computation is defined as usual except that the head never encounters an end to the tape as it moves leftward. Show that this type of Turing machine recognizes the class of Turing-recognizable languages. It suffices to convert a Turing machine with doubly infinite tape, M , into a regular Turing machine M accepting the same language. The idea is simply to “fold” the doubly-infinite tape over. If M has tape alphabet Γ and states Q , M will have tape alphabet Γ × Γ and states Q × { L, R } . M stores in tape location n two symbols: Location n of M and location n of M . The state space is doubled so that M can remember whether its simulating the left or right side of M ’s tape. The transition function is easily adapted.
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