5. 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
7. 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
8. 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.
9. 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 2q
Rba ,
............ ca
Time 1
1q
current state
10. 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.
11. A TM can be formally described as a 7-tuple
(Q, X, ∑, δ, q0, ♢, F) where,
Q is a finite set of states
X is the tape alphabet
∑ is the input alphabet
δ is a transition function; δ : Q × X → Q × X ×
{Left_shift, Right_shift}.
q0 is the initial state
♢ is the blank symbol
F is the set of final states
Formal Definition
12. Siraj Munir – CS@DSU
Comparison with Previous Models
16. Siraj Munir – CS@DSU
Comparison with Previous Models
Device Type of Grammar String/Language
Finite Automata Regular an
17. Siraj Munir – CS@DSU
Comparison with Previous Models
Device Type of Grammar String/Language
Finite Automata Regular an
Push Down Automata Context Free anbn
18. Siraj Munir – CS@DSU
Comparison with Previous Models
Device Type of Grammar String/Language
Finite Automata Regular an
Push Down Automata Context Free anbn
Turing Machine Unrestricted anbncn