06-turing-machines

06-turing-machines - Turing Machines A Turing machine is a...

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Turing Machines A Turing machine is a FA with an infinite tape as memory. Initially, the tape contains the input to the Turing machine. –p
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Church-Turing Thesis Why do we study Turing machines? Intuitive Notion of Algorithms equals Turing Machine Algorithms This equivalence cannot be proved but up to now no algorithm has been found that could not be implemented on a Turing machine. –p
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Turing Machines Example: Construct a TM, call it M 1 , that tests whether a string is a member of the language B = { u # u | u ∈{ 0 , 1 } } . That is, if some string w B then accept otherwise reject . Assume that the string w is loaded on the tape before the machine runs; the tape will look something like this for w = 101#101 , 101#101 t ... Algorithm: M 1 = “On input string w : 1. Zig-zag across the tape to corresponding positions on either side of the # symbol to check whether these positions contain the same symbol. If they do not, or if no # is found, reject . Cross off symbols as they are checked to keep track of which symbols
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06-turing-machines - Turing Machines A Turing machine is a...

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