What happens when a Turing machine halts?

In computability theory, a machine that always halts, also called a decider or a total Turing machine, is a Turing machine that eventually halts for every input. Because it always halts, such a machine is able to decide whether a given string is a member of a formal language.

Can a Turing machine accept an empty string?

If a TM(Turing Machine) accepts NO input string(even the blank), then its language is empty. If a TM ONLY accepts the blank string(meaning that there is nothing on the tape except for the default blank characters), then its language has only one item and it is the blank string.

What is blank tape halting problem?

The problem of finding an algorithm that, for any Turing machine, decides whether the machine eventually stops if it started on an empty tape; it has been proved that no such algorithm exists.

Why does a Turing machine need infinite tape?

A Turing machine has a tape of infinite length on which it can perform read and write operations. Assuming a black box, the Turing machine cannot know whether it will eventually enumerate any one specific string of the subset with a given program.

How did Alan Turing prove the halting problem?

In 1936, Alan Turing proved that the halting problem over Turing machines is undecidable using a Turing machine; that is, no Turing machine can decide correctly (terminate and produce the correct answer) for all possible program/input pairs.

Can the halting problem be solved?

It is a logical fact that the Halting problem is not “solvable” (by a turing machine).

Can TM accept Epsilon?

To give an example of mapping reductions, consider the following language: AE = \{ \langle M\rangle : M is a TM which accepts \epsilon\} . We will show that AE is not decidable. We will do this via a mapping reduction from ATM .

Can Turing machine have Epsilon transition?

An epsilon transition (also epsilon move or lambda transition) allows an automaton to change its state spontaneously, i.e. without consuming an input symbol. It may appear in almost all kinds of nondeterministic automaton in formal language theory, in particular: Nondeterministic Turing machine.

How can we reduce halting problem?

To reduce problem X to the Halting Problem:

1. Assume that you have an effective procedure (Turing machine or any other kind of algorithm) to solve problem X.
2. Show how to use the program for X to solve the Halting Problem.
3. Conclude that problem X can’t be solved.

Which Turing machine is like semi infinite tape?

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. Upper track − It represents the cells to the right of the initial head position.

Does a Turing machine have infinite memory?

Turing machines are similar to finite automata/finite state machines but have the advantage of unlimited memory. They are capable of simulating common computers; a problem that a common computer can solve (given enough memory) will also be solvable using a Turing machine, and vice versa.

Can humans solve halting problem?

Humans can’t solve the halting problem even for restricted cases where computers can, just imagine trying to analyze an otherwise trivial Turing machine that was larger than you could read in your lifetime. Turing machines are infinite and immortal, unlike us.

Can quantum computers solve the halting problem?

No, quantum computers (as understood by mainstream scientists) cannot solve the halting problem. We can already simulate quantum circuits with normal computers; it just takes a really long time when you get a decent number of qubits involved. (Quantum computing provides exponential speedups for some problems.)

What is HALT state in Turing machine?

Another special state is the halt state. The Turing machine’s computation ends when it enters its halt state. It is possible that a computation might never end because the machine never enters the halt state. This is analogous to an infinite loop in a computer program.

Why is halt TM undecidable?

and HALT are undecidable. There is no way to decide whether a TM will accept or eventually terminate. and HALT are recognizable. We can always run a TM on a string w and accept if that TM accepts or halts.

Can an NFA have an infinite loop?

Any infinite loop in an NFA must constitute only of ϵ transitions (since the input is finite, if the loop would have “eaten up” some letters, it must also be finite).

Can a DFA have empty transitions?

DFA doesn’t have epsilon transitions. If it had it, it could transit from current state to other state without any input i.e. with nothing , not even {} or phi.