How did Turing prove 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.
Why is the halting problem unsolvable?
But the halting problem is unsolvable, which means that it is impossible to test if an arbitrary Turing machine T halts on an arbitrary input x.
When did Turing prove the halting problem?
1936
The above problem is known as the halting problem and was famously proved by Alan Turing in 1936 to be uncomputable by the the formal definition of algorithms that he invented and its associated computational model, now popularly called the Turing machine.
Which of the problems are unsolvable by Turing machine?
One of well known unsolvable problems is the halting problem. It asks the following question: Given an arbitrary Turing machine M over alphabet = { a , b } , and an arbitrary string w over , does M halt when it is given w as an input? It can be shown that the halting problem is not decidable, hence unsolvable.
Can a human solve the halting problem?
Humans are “smart” because of smart algorithms that are cleverly written in neurons so computer scientists can’t steal or efficiently implement them. However clever these algorithms are, they most likely cannot reliably solve the halting problem.
What kind of problem is the halting problem?
unsolvable algorithmic problem is the halting problem, which states that no program can be written that can predict whether or not any other program halts after a finite number of steps. The unsolvability of the halting problem has immediate practical bearing on software development.
Is halting problem solvable?
Because the halting problem is not solvable on a Turing machine, it is not solvable on any computer, or by any algorithm, given the Church-Turing thesis. Many other unsolvability results are derived starting from the ones given here.
Which problem is un solvable?
Definition: A computational problem that cannot be solved by a Turing machine. The associated function is called an uncomputable function. See also solvable, undecidable problem, intractable, halting problem.
What makes a problem Undecidable?
In computability theory, an undecidable problem is a type of computational problem that requires a yes/no answer, but where there cannot possibly be any computer program that always gives the correct answer; that is, any possible program would sometimes give the wrong answer or run forever without giving any answer.
Is the halting problem solvable?
Is halting problem NP hard?
– If we had a polynomial time algorithm for the halting problem, then we could solve the satisfiability problem in polynomial time using A and X as input to the algorithm for the halting problem . – Hence the halting problem is an NP-hard problem which is not in NP. – So it is not NP-complete.