TM_high_level_description.docx - High Level Descriptions of...

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High Level Descriptions of Some Problems Solved by a TM (1) Decide the language {w#w|w€{0,1}*}. We need to match the symbols before # with symbols after #. One way is to zig-zag the corresponding places on the two sides of # and determine whether they match. Here is the algorithm for an input string w Stage 1: zig-zag across the tape to corresponding positions on either side of # to check whether these positions contain the same symbol. If they do not, or if no # is found, reject. Cross off symbols as they checked to keep track of which symbols correspond (you can use a symbol X) Stage 2: When all the symbols to the left of the # have been crosses off, check for any remaining symbols to the right of #. If any symbols remain , reject. Otherwise, accept. Note: If the symbol # is not given, then TM has to try all possible locations (just like PDA) for the middle of the string. (2) High level description of a 3-tape TM which when started with two binary integers separated by #, on its first tape computes their product (Assume that you have a TM which will add two numbers – it was discussed in the class under multi=track TM. I will call it ADDTM)
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  • Fall '15
  • Narendragoel
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