Turing Machines and Computability Theory

The main form of computability studied in computability theory was introduced by Turing (1936). A function f from natural numbers to natural numbers is a (Turing) computable, or recursive function if there is a Turing machine that, on input n, halts and returns output f(n). ...

1. What is a Turing machine and how is it related to automata theory?
2. What is the importance of Turing machine in theory of computation?
3. What is multidimensional Turing machine?
4. What is difference between restricted Turing Machine and Universal machine?
5. What are the applications of Turing machine?
6. What are the special features of Turing machine?
7. What is Turing machine with example?
8. Why Turing machine is most powerful?
9. What are the components of Turing machine?
10. How many types of Turing machines are there?
11. Which variant of Turing machine is more powerful?
12. What is meant by a Turing machine with two way infinite tape?

What is a Turing machine and how is it related to automata theory?

More specifically, it is a machine (automaton) capable of enumerating some arbitrary subset of valid strings of an alphabet; these strings are part of a recursively enumerable set. A Turing machine has a tape of infinite length on which it can perform read and write operations.

What is the importance of Turing machine in theory of computation?

Turing machines provide a powerful computational model for solving problems in computer science and testing the limits of computation — are there problems that we simply cannot solve? Turing machines are similar to finite automata/finite state machines but have the advantage of unlimited memory.

What is multidimensional Turing machine?

A multidimensional Turing machine has a multidimensional "tape;" for example, a two-dimensional Turing machine would read and write on an infinite plane divided into squares, like a checkerboard. ... A three-dimensional Turing machine might have possible directions N, E, S, W, U, D, and so on.

What is difference between restricted Turing Machine and Universal machine?

A universal Turing machine is just a Turing machine whose programming simulates other Turing machines. That is, the input to the UTM is a description of a Turing machine T and an input for T, and the UTM simulates T on that input. ... If you like, a UTM is an interpreter for (all) Turing machines.

What are the applications of Turing machine?

Turing machines founds applications in algorithmic information theory and complexity studies, software testing, high performance computing, machine learning, software engineering, computer networks and evolutionary computations.

What are the special features of Turing machine?

There are various features of the Turing machine: It has an external memory which remembers arbitrary long sequence of input. It has unlimited memory capability. The model has a facility by which the input at left or right on the tape can be read easily.

What is Turing machine with example?

Definition. A Turing Machine (TM) is a mathematical model which consists of an infinite length tape divided into cells on which input is given. It consists of a head which reads the input tape. ... If the TM reaches the final state, the input string is accepted, otherwise rejected.

Why Turing machine is most powerful?

But only a Turning machine can recognise a sequence that has an arbitrary number of As followed by the same number of Bs. That is a Turing machine is more powerful than a finite state machine because it can count.

What are the components of Turing machine?

A Turing machine consists of (a) a finite control, (b) one tape, representing the memory, that has a left margin and is divided into an infinite number of cells, and (c) a moving read/write head. The finite control can be in any one of a finite set Q of states.

How many types of Turing machines are there?

Answer Expert Verified. The different types of turing machines are: Turing machines with two-dimensional tapes – They have one read-write head, one finite control and one two-dimensional tape. Turing machines with multiple tapes – They have one finite control and over one tape with a read-write head for each tape.

Which variant of Turing machine is more powerful?

Explanation: The multitape turing machine model seems much powerful than the single tape model, but any multi tape machine, no matter how many tapes, can be simulated by single taped TM.

What is meant by a Turing machine with two way infinite tape?

A two-way infinite tape Turing machine (TTM) is a Turing machine with its input tape infinite in both directions, the other components being the same as that of the basic model. We see in the following theorem that the power of TTM is no way superior of that of the basic TM.