39+Slides--More+on+Turing+Machines

39+Slides--More+on+Turing+Machines - CS103 HO#39...

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Unformatted text preview: CS103 HO#39 Slides--More on Turing Machines 5/6/11 1 q b b a b b Multi-tape Turing Machines 0 1 0 0 0 1 1 x y x z z z # b b a b b # 0 1 0 0 0 1 1 0 # x y x z z z # q Every multi-tape Turing machine has an equivalent single-tape Turing machine. Every multi-tape Turing machine has an equivalent single-tape Turing machine. We must show: • If L is a language recognized by a multitape Turing machine, there is a single-tape Turing machine that recognizes L. • If L is a language recognized by a single-tape Turing machine, there is a multitape Turing machine that recognizes L. Typically, one direction of these proofs is easy. Here, a single-tape machine is a special case of a multi-tape machine. The importance: we know that a language is Turing-recognizable if we can design a multitape Turing machine that recognizes it. q b b a b b Multi-tape Turing Machines 0 1 0 0 0 1 1 x y x z z z b b a b b 0 1 0 0 1 1 0 x y x z z z z q 1 2 3 alphabet = 1 2 3 Nondeterministic Turing Machines : Q P (Q {L, R}) C = q w C 1 C 2 C 12 C 11 C 21 C 3 C 31 C 31 C 31 . . . . . . . . . Simulate with a three-tape machine:-- input tape (does not change)-- working tape (used in the computations)-- address tape (to remember where we are in the tree) Do a breadth-first search rather than a depth-first search Variants of Turing Machines Doubly Infinite Tape control a b b a b b Turing Machine with left reset : Q Q {R, RESET} control a b b a b b Variants of Turing Machines CS103 HO#39 Slides--More on Turing Machines 5/6/11 2 Detailed Design To move left: Mark current position Reset Shift the tape one square to the right (but not the mark) Reset Scan right to mark a b b a b b becomes a b b a b b Turing Machine with 2-dimensional tape : Q Q {L, R, U, D} control Keep the portion of the tape the has been visited on a one-dimensional tape We express the fact that the power of Turing machines does not change with all these variations by saying that this is a robust model of computation....
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39+Slides--More+on+Turing+Machines - CS103 HO#39...

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