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l10-handout - Outline Multiple tapes Lecture 10:...

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Lecture 10: Decidability David Dill and C´esar S´anchez Department of Computer Science 1 Outline Multiple tapes Non-deterministic TMs Weakening the TM model semi-infinite tape multi-stack PDAs three-counter machines two-counter machines P vs. NP Recursively enumerable and Recursive languages 2 Extensions to Turing Machines Since Turing machines are already as powerful as any real model of computation can be, adding stuff to them doesn’t increase their power. It rarely even speeds them up all that much. Multi-tape Turing Machine It has k tapes, each with a separate head. The input is on the first tape with the head on the first non-blank. All other tapes are blank, and the heads are in arbitrary positions (doesn’t matter). The transition function depends on the state and currently scanned symbol on each tape, and updates the state and writes a new symbol on each tape and moves each head. Each head can also remain stationary instead of moving left or right. Everything else is the same. 3 Equivalence of Single and Multi-Tape Turing Machines (I’ll present the basic ideas. Details are in the book.) Obviously, an MTTM can do anything a single-tape TM can do. Construction in the other direction: Create a TM N that simulates a MTTM M as follows: N is a multi-track (but single tape) machine. Use 2 tracks for each simulated tape. One track has the tape contents, the other has a marker for the head position. To simulate a move of
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This note was uploaded on 03/08/2011 for the course CS 154 taught by Professor Motwani,r during the Winter '08 term at Stanford.

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l10-handout - Outline Multiple tapes Lecture 10:...

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