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

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

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

### Page1 / 5

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online