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Lecture Notes on Turing Machine - Senior Seminar | CSC 490, Study notes of Computer Science

Material Type: Notes; Professor: Locklair; Class: Senior Seminar; Subject: Computer Science; University: Concordia University - Wisconsin; Term: Fall 2006;

Typology: Study notes

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Uploaded on 07/23/2009

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6 November – Day 21
Turing Machine is a fundamental CS concept
Turing – Alan Turing ~1900-1955, British mathematician
wanted to solve the ‘universal computation’ problem
TM is a mathematical model of computation (collection of rules)
Importance of TM comes from the Turing Thesis which says:
TM is the “simplest” computer – anything a computer can do can be
done by a TM!
Follow handout (chapter 9 of Peter Linz, MCS 825 text)
p. 230 –
draw tape – tape consists of cells which may contain a symbol
draw read/write head –
I/O
- - - - -
control unit Processing
[note: Linz moves read/write head while Dewdney will move the tape]
TM model (picture fig 9.1)
Control unit is really a black box
“Outward” appearance, operation is simple
1. Move tape R or L
2. Read symbol off of tape
3. Write a new symbol on the tape
(tape is storage)
Power of a TM comes from what’s “inside” the control unit
- a “state machine”
Control unit
Q = {set of internal states}
q0 = initial state
F = final state(s)
delta = transition function
Control unit of a TM is specified by (key) state transition functions,
delta
CSC 490 Course Notes and Outline, © Dr. Gary Locklair, Fall 2006
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6 November – Day 21 Turing Machine is a fundamental CS concept Turing – Alan Turing ~1900-1955, British mathematician wanted to solve the ‘universal computation’ problem TM is a mathematical model of computation (collection of rules) Importance of TM comes from the Turing Thesis which says: TM is the “simplest” computer – anything a computer can do can be done by a TM! Follow handout (chapter 9 of Peter Linz, MCS 825 text) p. 230 – draw tape – tape consists of cells which may contain a symbol draw read/write head – I/O


control unit Processing [note: Linz moves read/write head while Dewdney will move the tape] TM model (picture fig 9.1) Control unit is really a black box “Outward” appearance, operation is simple

  1. Move tape R or L
  2. Read symbol off of tape
  3. Write a new symbol on the tape (tape is storage) Power of a TM comes from what’s “inside” the control unit
    • a “state machine” Control unit Q = {set of internal states} q0 = initial state F = final state(s) delta = transition function Control unit of a TM is specified by (key) state transition functions, delta CSC 490 Course Notes and Outline, © Dr. Gary Locklair, Fall 2006

Ex: delta (q0, a) = read as (IF) current state is [q0] and read this symbol [a] off tape, (THEN) = (q1, d, R) move to state [q1], write new symbol [d], and move tape [R] TM’s control unit is a collection of many state transition functions Follow through example 9.2 and 9. Visit TM simulator site at www.cs.brown.edu/people/ng/Turing/tmachine.html We have “Visual Turing” installed Chapter 31 in Dewdney Some “insights” into TMs A TM is essentially the same thing as its program (control unit transition functions) Figure 31. note: his quintuple is really same as Linz transition function (q, s, q’, s’, d) current state, current symbol, new state, new symbol, direction to move tape high-level explanation of Multiplication unary system large “program” figure 31.2 beginning and end for next time – read and follow “multiplication” problem in Dewdney Presentations next time CSC 490 Course Notes and Outline, © Dr. Gary Locklair, Fall 2006