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Turing Machines
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Turing Machines - Computability - Lecture Slide, Slides of Computer Science
Some concepts of Computability are Algorithmic Problems, Automata, Closure of Regular Languages, Computability, Free Languages, Machine Transforms, Magic Bullets, Minimization, Models of Computation, Nondeterministic Complexity. Important points in this lecture are: Turing Machines, Alan Turing, Motivation, Church-Turing Thesis, Definitions, Computation, Recognizers Deciders, Turing Machine, Instrumental in Cracking, Turing Award
Typology: Slides
2012/2013
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Turing Machines
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Agenda
Turing Machines
Alan Turing Motivation Church-Turing Thesis Definitions Computation TM Configuration Recognizers vs. Deciders
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First Goal of Turing’s Machine: A model that can compute anything that a human can compute. Before invention of electronic computers the term “computer” actually
referred to a person who’s line of work is to
calculate numerical quantities!
As this is a philosophical endeavor, it can’t really be proved.
Turing’s Thesis: Any “algorithm” can be carried out by one of his machines
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Second Goal of Turing’s Machine: A model that’s so simple, that can actually prove interesting epistemological results. Eyed Hilbert’s 10th^ problem, as well as a computational analog of Gödel’s Incompleteness Theorem in Logic.
Philosophy notwithstanding, Turing’s programs for cracking the Enigma cryptosystem prove that he really was a true hacker! Turing’s machine is actually easily programmable, if you really get into it. Not practically useful, though… Docsity.com
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EG Successor Program
Sample Rules:
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read •, write 1, HALT!
Let’s see how they are carried out on a
piece of paper that contains the
reverse binary representation of 47:
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EG Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read •, write 1, HALT!
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EG Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read •, write 1, HALT!
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EG Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read •, write 1, HALT!
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EG Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read •, write 1, HALT!
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EG Successor Program
So the successor’s output on 111101 was
000011 which is the reverse binary
representation of 48.
Similarly, the successor of 127 should be
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EG Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read •, write 1, HALT!
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EG Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read •, write 1, HALT!
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EG Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read •, write 1, HALT!
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