**(1) What is Multi-Head Turing Machine?**

A k-head TM has some k heads. The heads are numbered 1
through k, and move of the TM depends on the state and on the symbol scanned by
each head. In one move, the heads may each move independently left or right or
remain stationary.

**(2) ****What is a 2-way infinite tape TM ?**

In 2-way infinite tape TM, the tape is infinite
in both directions. The leftmost square is not distinguished. Any computation
that can be done by 2-way infinite tape can also be done by standard TM.** **

**(3) ****What is a Multi-tape Turing machine?**

A multi-tape Turing machine consists of a finite control
with k-tape heads and k tapes ; each tape is infinite in both directions. On a
single move depending on the state of finite control and symbol scanned by each
of tape heads ,the machine can change state print a new symbol on each cells
scanned by tape head, move each of its tape head independently one cell to the
left or right or remain stationary.

**(4) What is a Multidimensional TM****?**

** **

The device has a finite control , but the tape
consists of a k-dimensional array of cells infinite in all 2k directions, for
some fixed k. Depending on the state and symbol scanned , the device changes
state , prints a new symbol and moves its tape head in one of the 2k directions,
either positively or negatively ,along one of the k-axes**.**

** **