It is also easy to see that the halting problem is not in NP since all problems in NP are decidable in a finite number of operations, but the halting problem, in general, is undecidable . There are also NP-hard problems that are neither NP-complete nor Undecidable.
Are halts NP?
@djhaskin987 The halting problem is not NP-complete (because, as you note, it is not decidable thus not in NP), but it is NP-hard (that is, at least as hard as everything in NP after a polynomial-time reduction) because every decision problem can be reduced to it.
Is Halting Problem complete?
The halting problem is a decision problem about properties of computer programs on a fixed Turing-complete model of computation, i.e., all programs that can be written in some given programming language that is general enough to be equivalent to a Turing machine.
Which problem is NP problem?
A problem is called NP ( nondeterministic polynomial ) if its solution can be guessed and verified in polynomial time; nondeterministic means that no particular rule is followed to make the guess. If a problem is NP and all other NP problems
Why is halting a 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.
How do you prove halting problems?
Proof: Assume to reach a contradiction that there exists a program Halt(P, I) that solves the halting problem, Halt(P, I) returns True if and only P halts on I. The given this program for the Halting Problem, we could construct the following string/code Z: Program (String x) If Halt(x, x) then Loop Forever Else Halt.
What is the halting problem an example of?
The halting problem is an early example of a decision problem , and also a good example of the limits of determinism in computer science.
What is NP-hard problem with example?
Examples. An example of an NP-hard problem is the decision subset sum problem : given a set of integers, does any non-empty subset of them add up to zero? That is a decision problem and happens to be NP-complete.
Why is knapsack problem NP-hard?
the time needed increases in exponential term, so it’s a NPC problem. This is because the knapsack problem has a pseudo-polynomial solution and is thus called weakly NP-Complete (and not strongly NP-Complete).
How do you solve NP-hard problems?
NP-Hard problems(say X) can be solved if and only if there is a NP-Complete problem(say Y) that can be reducible into X in polynomial time. NP-Complete problems can be solved by a non-deterministic Algorithm/Turing Machine in polynomial time . To solve this problem, it do not have to be in NP .
Can humans solve the 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. ... Every case a computer can solve the halting problem a human can as well, it may just take longer.
What are the unsolvable problems?
Definition: A computational problem
Is it possible for a problem to be in both P and NP?
Is it possible for a problem to be in both P and NP? Yes . Since P is a subset of NP, every problem in P is in both P and NP.
Can an undecidable problem ever be solved?
Definition: A decision problem is a problem that requires a yes or no answer. Definition: A decision problem that admits no algorithmic solution is said to be undecidable. No undecidable problem can ever be solved by a computer or computer program of any kind . ... It means we can never find an algorithm for the problem.
How is halting problem undecidable?
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 halting problem unsolvable?
Rice’s theorem generalizes the theorem that the halting problem is unsolvable. It states that for any non-trivial property , there is no general decision procedure that, for all programs, decides whether the partial function implemented by the input program has that property.
