Transcript
Welcome!!
Siraj Munir – CS@DSU
Introduction To Turing Machine
Siraj Munir – CS@DSU
Tip of The Day
discourager.ignore();
(Courtesy: Syed Hammad Ahmed – CS@DSU)
Background
Siraj Munir – CS@DSU
Background• Finite Automata accepts regular languages only.
For example: {anbn : n = 0, 1, …} is not regular, but it is context free language.
• Pushdown Automata accepts context-free languages only.For example: {anbncn : w *} is not context-free.
What to do??
Siraj Munir – CS@DSU
Turing Machines
About:
• Introduced by Alan Turing in 1936.
• A simple mathematical model of a computer.
• Models the computing capability of a computer.
Siraj Munir – CS@DSU
Siraj Munir – CS@DSU
a1 a2 ….
Control
head
Tape
Informal Description
The head:• Reads the symbol from the cell it is pointing to, • Either:
• Writes a new symbol in the cell, or• Moves one cell to the left or right.
Siraj Munir – CS@DSU
Informal Description (II)
• New cells can be added to the right of the tape as needed (similar to RAM memory)
• These new cells contain the blank symbol, ♢
1q 2qRba ,
............ ca
Time 1
1qcurrent state
Siraj Munir – CS@DSU
• Transitions can be described by (Case I):
((s,a),(q;b;R)) If the machine is in state s and the current cell has an a then jump to state q and write b in the current cell and moves head to right.
Formal Description
• Transitions can be described by (Case II):
((s,a),(q;b;L)) If the machine is in state s and the current cell has an a then jump to state q and write b in the current cell and moves head to left.
A TM can be formally described as a 7-tuple (Q, X, ∑, δ, q0, ♢, F) where,Q is a finite set of statesX is the tape alphabet∑ is the input alphabetδ is a transition function; δ : Q × X → Q × X × {Left_shift, Right_shift}.q0 is the initial state♢ is the blank symbolF is the set of final states
Formal Definition
Siraj Munir – CS@DSU
Comparison with Previous Models
Machine Data Structure Deterministic?
Finite Automata N.A Yes
Pushdown Automata
Turing Machine
Siraj Munir – CS@DSU
Machine Data Structure Deterministic?
Finite Automata N.A Yes
Pushdown Automata Stack (LIFO) No
Turing Machine
Siraj Munir – CS@DSU
Machine Data Structure Deterministic?
Finite Automata N.A Yes
Pushdown Automata Stack (LIFO) No
Turing Machine Infinite Tape Yes
Siraj Munir – CS@DSU
Siraj Munir – CS@DSU
Comparison with Previous ModelsDevice Type of Grammar String/Language
Finite Automata Regular an
Siraj Munir – CS@DSU
Comparison with Previous ModelsDevice Type of Grammar String/Language
Finite Automata Regular an
Push Down Automata Context Free anbn
Siraj Munir – CS@DSU
Comparison with Previous ModelsDevice Type of Grammar String/Language
Finite Automata Regular an
Push Down Automata Context Free anbn
Turing Machine Unrestricted anbncn
Siraj Munir – CS@DSU
Questions??
Siraj Munir – CS@DSU
Reference:
http://www.slideshare.net/abhishiv77/push-down-automata-vs-turing-machine
http://www.slideshare.net/AyAnKhAn5/turing-machine-34338253
http://www.slideshare.net/dkalita3/turing-machine-bydeep
http://www.slideshare.net/lavishka_anuj/turing-machines-12176328
https://en.wikipedia.org/wiki/Turing_machine
Siraj Munir – CS@DSU
Thankyou!
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