• Share
  • Email
  • Embed
  • Like
  • Save
  • Private Content
Computer Science Fundamentals - Turing Machines
 

Computer Science Fundamentals - Turing Machines

on

  • 1,046 views

 

Statistics

Views

Total Views
1,046
Views on SlideShare
1,031
Embed Views
15

Actions

Likes
2
Downloads
30
Comments
0

2 Embeds 15

http://lanyrd.com 14
https://twitter.com 1

Accessibility

Categories

Upload Details

Uploaded via as Adobe PDF

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

    Computer Science Fundamentals - Turing Machines Computer Science Fundamentals - Turing Machines Presentation Transcript

    • ComputerScienceFoundationsTuring Machine EditionJason DewGeezeo / Catamorphic Labs
    • AlanTuring
    • Entscheidungsproblem David Hilbert
    • Alphabetany set of symbolsexamples:● {a, b, c, d, ..., z}● {0, 1, 2, 3, ..., 9}● {0, 1}
    • Stringsequence of symbols from the alphabetexamples:● foobar● 0101001● (empty string)
    • Formal Languageany set of strings over an alphabetexamples:● {foo, bar, baz}● {00, 01, 10, 11}● {b, ab, aab, aaab, aaaab, ... }
    • DeterministicFinite Automata http://15mmvsf.bagofmice.com/vsf/prev_robot.htm
    • Formal Definition● an alphabet● a set of states ○ one denoted as a "starting state" ○ one or more denoted as "accepting states"● a transition function ○ takes a symbol and a state and returns a new state
    • DFA acceptingmultiples of 3
    • NondeterministicFinite Automata
    • Formal Definition● an alphabet● a set of states ○ one denoted as a "starting state" ○ one or more denoted as "accepting states"● a transition function ○ takes a symbol and a state and returns zero or more states
    • Example NFA
    • Theorem Any NFA can be converted into an equivalent DFA.
    • Regular Language Any language which can be recognized by some finite automaton.
    • Regular Expressions
    • Theorem A language is regular if and only if some regular expression describes it.
    • Turing machines
    • Formal Definition (slightly simplified)● two alphabets ○ one for reading, the input alphabet ○ one for writing, the output (or tape) alphabet● a set of states ○ one starting state ○ one accepting state ○ one rejecting state● a transition function takes a symbol and a state and returns a new state, a symbol to write, and Left or Right
    • Example TMLets call it MIt accepts strings whose length is a power of 2Accepted strings: "0", "00", "0000"Rejected strings: "", "000", "000000"
    • A description of M Attribution: Sipser, Figure 3.8
    • Running on "00" tape state .00_ q1 _.0_ q2 _x._ q3 _.x_ q5 ._x_ q5 _.x_ q2 _x._ q2 _x_. qaccept
    • Running on "0000"tape state.0000_ q1 tape state_.000_ q2 _.x0x_ q2_x.00_ q3 _x.0x_ q2_x0.0_ q4 _xx.x_ q3 tape state_x0x._ q3 _xxx._ q3 _.xxx_ q2_x0.x_ q5 _xx.x_ q5 _x.xx_ q2_x.0x_ q5 _x.xx_ q5 _xx.x_ q2_.x0x_ q5 _.xxx_ q5 _xxx._ q2._x0x_ q5 ._xxx_ q5 _xxx_. qaccept
    • Wrapping upWhy do we care about Turing machines?
    • ReferencesDeterministic finite automaton. (2012, March 11). Retrieved from http://en.wikipedia.org/wiki/Deterministic_finite_automatonNondeterministic finite automaton. (2012, April 20). Retrieved from http://en.wikipedia.org/wiki/Nondeterministic_finite_automatonPetzold, C. (2008). The annotated turing. Indianapolis: Wiley Publishing, Inc.Sipser, M. (2006). Introduction to the theory of computation. (2nd ed.). Boston:Thompson Course Technology.Turing machine. (2012, April 17). Retrieved from http://en.wikipedia.org/wiki/Turing_machine
    • Come work with me!