06s - MCS-265 David Wolfe Homework set 6 solution April 14,...

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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 infnite tape is similar to an ordinary Turing machine except that its tape is inFnite to the left as well as to the right. The tape is initially Flled with blanks except for the portion that contains the input. Computation is deFned 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 inFnite tape, M , into a regular Turing machine M 0 accepting the same language. The idea is simply to “fold” the doubly-inFnite tape over. If M has tape alphabet Γ and states Q , M 0 will have tape alphabet Γ × Γandstates Q ×{ L,R } . M 0 stores in tape location n two symbols: Location n of M and location n of M . The state space is doubled so that M 0 can remember whether its simulating the left or right side of M ’s tape. The transition function is easily adapted.
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This note was uploaded on 02/22/2010 for the course CS 881 taught by Professor H.f. during the Spring '10 term at Shahid Beheshti University.

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