Variants of Turing Machines

1. Multiple track Turing Machine: 
 

• A k-track Turing machine(for some k>0) has k-tracks and one R/W head that reads and writes all of them one by one.
• A k-track Turing Machine can be simulated by a single track Turing machine

2. Two-way infinite Tape Turing Machine: 
 

• Infinite tape of two-way infinite tape Turing machine is unbounded in both directions left and right.
• Two-way infinite tape Turing machine can be simulated by one-way infinite Turing machine(standard Turing machine).

3. Multi-tape Turing Machine: 

• It has multiple tapes and is controlled by a single head.
• The Multi-tape Turing machine is different from k-track Turing machine but expressive power is the same.
• Multi-tape Turing machine can be simulated by single-tape Turing machine.

4. Multi-tape Multi-head Turing Machine: 
 

• The multi-tape Turing machine has multiple tapes and multiple heads
• Each tape is controlled by a separate head
• Multi-Tape Multi-head Turing machine can be simulated by a standard Turing machine.

5. Multi-dimensional Tape Turing Machine: 
 

• It has multi-dimensional tape where the head can move in any direction that is left, right, up or down.
• Multi dimensional tape Turing machine can be simulated by one-dimensional Turing machine

6. Multi-head Turing Machine: 
 

• A multi-head Turing machine contains two or more heads to read the symbols on the same tape.
• In one step all the heads sense the scanned symbols and move or write independently.
• Multi-head Turing machine can be simulated by a single head Turing machine.

7. Non-deterministic Turing Machine: 
 

• A non-deterministic Turing machine has a single, one-way infinite tape.
• For a given state and input symbol has at least one choice to move (finite number of choices for the next move), each choice has several choices of the path that it might follow for a given input string.
• A non-deterministic Turing machine is equivalent to the deterministic Turing machine.

Restricted TMs

• Turing Machine accepts the recursively enumerable language. It is more powerful than any other automata such as FA, PDA, and LBA. It computes the partial recursive function. It can be further divided into Deterministic Turing Machine(DTM) or Non-Deterministic Machine(NTM). By default, Turing Machine is DTM, and the power of DTM and NTM are the same.
• This machine acts as a Recognizer or Acceptor and as an Enumerator.
• The machine is said to be as acceptor which accepts or recognizes the strings of a recursively enumerable language (L) over the input alphabet(∑ ) and the machine is said to be as enumerator which enumerates the string of recursively enumerable language over the input alphabet ∑.

The restricted Turing machines can be of the following types :

1. Halting Turing Machine :
   A Turing Machine is said to be a halting Turing machine if it always halts for every input string. It can accept the recursive language and is less powerful than Turing machine.
2. Linear Bounded Automata :
   It behaves as a Turing machine but the storage space of tape is restricted only to the length of the input string. It is less powerful than a Turing machine but more powerful than push down automata.
3. Unidirectional Turing Machine :
   The head of this type of turing machine can move only in one direction. It can accept the only regular language. It has the same power as finite automata but less powerful than push down automata.
4. Read Only Turing Machine :
   It is equivalent to finite automata. It contains a read head only which doesn’t have written capability. It accepts only regular languages.
5. Read Only-Unidirectional Turing Machine :
   It is similar to finite automata. It contains a read-only head and can move only in one direction. It accepts a regular language.