The document summarizes the Turing machine. It describes a Turing machine as having three main elements: an input/output tape, a read/write head that moves bidirectionally along the tape, and a finite state control. It operates by examining the symbol under the head along with its current state to determine the symbol to write, the head's movement, and the next state. The document then provides a formal definition of a Turing machine as a 7-tuple and describes some variations including those with different tape configurations and those that are nondeterministic or have multiple tapes/heads.

1. Math- I, II, III, IV, RSA & TCS by Parmar Sir [9764546384]
MU | Comp/IT | TCS/AT | Push Down Automata | Feb 2014 | Parmar Sir Page 1
Turing Machine [TM]
 Turing machine (Working Principle)
 Turing machine is a simple mathematical model of a general purpose computer.
 Turing machine models, computing power equivalent to a computer i.e. the Turing machine is
capable of performing any calculation which can be performed by any computing machine.
 The TM will have three elements
1. Input/ Output Tape
2. Read write head which is bidirectional.
3. Finite state Control
Finite State Control
aaa b b
Input / Output
TapeRead / Write
Head
BB
Bidirectional
 The Turing machine can be thought of as a finite automata connected to read/ write head which is
bidirectional i.e. can be move left to write and write to left.
 It has o ne input / output tape which is divided in many cells. At each cell only one input symbol is
placed.
 The input and output on tape affected by the read/ write head which can examine one cell in one
move.
 In one move, the machine examine the present symbol under the read/ write head on the tape and
the present state of an automaton to determine
 What to do with tape present symbol i.e. a new symbol to be written or no change of symbol
on the tape in the cell.
 In which direction head move i.e. either the head moves one cell left (L), or one cell right (R),
or stay at the same cell (N).
 The next state of machine.
 TM is more powerful than other all machines.
 TM is used for recognizing all type languages especially for Type-0 and Type-1.

2. Math- I, II, III, IV, RSA & TCS by Parmar Sir [9764546384]
MU | Comp/IT | TCS/AT | Push Down Automata | Feb 2014 | Parmar Sir Page 2
 Turing machine Definition
A Turing machine is 7 tuple automata
Where
Q is a finite set of states
finite set of input symbol
finite nonempty set of tape symbol
the initial state.
special tape symbol representing blank .
is a final accepting state
The transition function of TM
 Different Type Or variations of Turing Machine
1. Turing machine with two way Infinite Tape
As it name implies, the tape is infinite to the left as well as to the right, we imagine that there is
infinity of blank cells to the left and the right of the current nonblank portion of the tape.
A language L is recognized by a Turing machine with a one-way infinite tape.
2. Turing machine with semi-infinite tapes
In TM head can move either left or right from its initial position. In semi-infinite tapes TM’s
head only allowed to move within the position at and to the right of the initial head position.
In TM with semi-infinite tapes there are no cells to the left of the initial position.
3. Multi-tape Turing machine
4. Multi-head Turing machine
5. Multi-dimensional Turing Machine
6. Nondeterministic Turing machine
7. Composite Turing machine
8. Iterated Turing machine