Transcript
Conceptually a Turing machine, like finite automata
A Turing machine consists of a finite-state control unit and a tape that is infinite in both directions and divided into cells, each of which can hold one symbol:
At each step, the control unit performs two actions in a way dependent on:
The two actions will be: 1. either – move the read/write head one cell to the left or
right; 2. put the control unit into a new state
Turing machine will be your ultimate model for computer.In Turing machine output is very important.We know that every program has an output but this is not exactly true.
1.READ X 2.IF X=1 THEN END 3.IF X=2 THEN DIVIDE X BY 0 4.IF X>2 THEN GOTO STATEMENT 4 We shall see in a moment that the same
terminology is applied to Turing machine.
............
Read-Write head
Control Unit
............
Read-Write head
No boundaries -- infinite length
The head moves Left or Right
............
Read-Write head
The head at each transition (time step):
1. Reads a symbol 2. Writes a symbol 3. Moves Left or Right
............
Example:Time 0
............Time 1
1. Reads
2. Writes
a a cb
a b k c
a
k3. Moves Left
............Time 1
a b k c
............Time 2
a k cf
1. Reads
2. Writes
bf
3. Moves Right
............
Blank symbol
head
a b ca
Head starts at the leftmost positionof the input string
Input string
1q 2qLba ,
Read Write Move Left
1q 2qRba ,
Move Right
Definition. A Turing machine is a 7-tuple (Q, , , , q0, qaccept, qreject),
where:• Q is a set of states
is a set of symbols (the alphabet)
is a set of symbols that can be written in tape, and
• q0 Q is the initial state
• qaccept is the accepting state
• qreject is the rejecting state, qreject qaccept
is a collection of transitions defined by the function:
: (Q {qaccept, qreject }) Q {, }
The machine halts in a state if there isno transition to follow
Halting Example 1:
............ a b ca
1q
1q No transition from
HALT!!!
1q
1q 2q Allowed
1q 2q Not Allowed
•Accepting states have no outgoing transitions•The machine halts and accepts
Accept Input If machine halts in an accept state
Reject Input
If machine halts in a non-accept state or If machine enters an infinite loop
string
string
Accepts the language: *a
0q
Raa ,
L,1q
Input alphabet },{ ba
aaTime 0
0q
a
0q
Raa ,
L,1q
aaTime 1
0q
a
0q
Raa ,
L,1q
aaTime 2
0q
a
0q
Raa ,
L,1q
aaTime 3
0q
a
0q
Raa ,
L,1q
aaTime 4
1q
a
0q
Raa ,
L,1q
Halt & Accept
Rejection Example
0q
Raa ,
L,1q
baTime 0
0q
a
0q
Raa ,
L,1q
baTime 1
0q
a
No possible Transition
Halt & Reject
Accepts the language: *a
0q
but for input alphabet }{aA simpler machine for same language
aaTime 0
0q
a
0q
Halt & Accept
Not necessary to scan input
Turing machine as a language recognizer.
Turing machine as a language generator.
Turing machine as a language evaluator.
Turing machine as a language decider.
ANY QUESTIONS??
top related