What are the Turing machine variations in TOC?

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Turing machines (TM) can also be deterministic or non-deterministic, but this does not make them any more or less powerful.

However, if the tape is restricted so that you can only see use of the part of the tape with the input, the TM becomes less powerful (linear bounded automata) and can only recognise context sensitive languages.

Many other TM variations are equivalent to the original TM. This includes the following −

  • Multi-track

  • Multi-tape

  • Multi-head

  • Multi-dimensional tape

  • The off-line Turing machine

Multi-tape Turing Machine

A Turing machine with several tapes we call it a multi tape Turing machine.

Every tape’s have their own Read/Write head

For N-tape Turing Machine

M={( Q,X, ∑,δ,q0,B,F)}

We define

δ=QxXN ->Q x XN x {L,R}N


If n=2 with current configuration δ(q0,a,e)=(q1,X,Y,L,R)

δ=QxXN ->Q x XN x {L,R}N

Non Deterministic Turing Machine

It is similar to DTM except that for any input and current state it has a number of choices.

A string is accepted by a NDTM if there is a sequence of moves that leads to a final state

The Transition function −

=Q x X ->2QxXx(L,R) 

A NDTM is allowed to have more than one transition for a given tape symbol.

Multi-head Turing machine

It has a number of heads instead of one.

Each head independently reads/ writes symbols and moves left/right or keeps stationery.

Off-line Turing Machine

An offline Turing machine has two tapes, which are as follows −

  • One tape is read-only and contains the input.

  • The other is read-write and is initially blank.

Published on 16-Jun-2021 12:39:22