Compiler construction

1. Variants of Turing Machine
WEEK: 16
LECTURE: 2
Program: BS CS/SE 5th Semester
Course: CS563 THEORY OF AUTOMATA

2. Introduction
• There are a number of other types of Turing
machines
• Computationally all these Turing machines are
equally powerful.
• what one type can compute any other can also
compute.
• However, the efficiency of computation, that is,
how fast they can compute, may vary.

3. Multi-tape Turing Machine
• A multi-tape Turing machine is like an
ordinary Turing machine with several tapes
• Each head can move independently of the
other heads
• Each tape has its own head for reading and
writing
• Initially the input is on tape 1 and others are
blank
• At first, the first tape is occupied by the input
and the other tapes are kept blank

4. Cont.
• Machine reads consecutive symbols under its
heads and TM prints a symbol on each tape &
moves its heads
• This model intuitively seems much more
powerful than single-tape model, but any multi-
tape machine, no matter how many tapes, can
be simulated by a single-tape machine
• Multi-tape machines cannot calculate any more
functions than single-tape machines

5. Example
Convert multiple TM M to an
equivalent single-tape TM S
• Let M has k tapes. S simulated the
effect of k tapes by storing their
information on its single tape
• Requires new symbol # as a
delimiter
• S must keep track of the locations of
all heads
• A dotted symbol represent the head
position

6. Multi-track TM
• contain multiple tracks but just one tape head
reads and writes on all tracks
• a single tape head reads n symbols
from n tracks at one step

7. Non-Deterministic Turing
Machine
• For every state and symbol, there are a group of
actions the TM can have.
• So, here the transitions are not deterministic.
• The computation of a non-deterministic Turing
Machine is a tree of configurations that can be
reached from the start configuration

8. Cont.…
• An input is accepted if there is at least one
node of the tree which is an accept
configuration, otherwise it is not accepted.
• If all branches of the computational tree halt
on all inputs, the non-deterministic Turing
Machine is called a Decider and if for some
input, all branches are rejected, the input is
also rejected.

9. Semi-infinite Turing Machine
• A Turing Machine with a semi-infinite tape has
a left end but no right end
• The left end is limited with an end marker
• It is a two-track tape −
• Upper track − It represents the cells to the right of the
initial head position
• Lower track − It represents the cells to the left of the
initial head position in reverse order