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What do you mean by halting problem?
The halting problem, commonly applied to Turing-complete programs and models, is the problem of finding out whether, with the given input, a program will halt at some time or continue to run indefinitely.
Is halting problem decidable?
The halting problem is theoretically decidable for linear bounded automata (LBAs) or deterministic machines with finite memory. A machine with finite memory has a finite number of configurations, and thus any deterministic program on it must eventually either halt or repeat a previous configuration: …
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.
How to solve halting problem?
Halting problem is perhaps the most well-known problem that has been proven to be undecidable; that is, there is no program that can solve the halting problem for general enough computer programs. It’s important to specify what kind of computer programs we’re talking about.
What is Undecidability explain with halting problem?
Alan Turing proved in 1936 that a general algorithm running on a Turing machine that solves the halting problem for all possible program-input pairs necessarily cannot exist. Hence, the halting problem is undecidable for Turing machines.
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.
Is halting problem recursively enumerable?
The language HALT corresponding to the Halting problem is recursively enumerable, but not recursive. In particular, the universal TM accepts HALT, but no TM can decide HALT. There are languages which are not recursively enumerable, in particular the language NOTRE in the proof.
Can an algorithm solve an undecidable problem?
Created by Pamela Fox. Some problems take a very long time to solve, so we use algorithms that give approximate solutions. An undecidable problem is one that should give a “yes” or “no” answer, but yet no algorithm exists that can answer correctly on all inputs.
What types of problems are undecidable?
There are some problems that a computer can never solve, even the world’s most powerful computer with infinite time: the undecidable problems. An undecidable problem is one that should give a “yes” or “no” answer, but yet no algorithm exists that can answer correctly on all inputs.
What does halting mean in theory of computation?
Basically halting means terminating. So can we have an algorithm that will tell that the given program will halt or not. In terms of Turing machine, will it terminate when run on some machine with some particular given input string.
What does it mean when a program halts?
Halting means that the program on certain input will accept it and halt or reject it and halt and it would never go into an infinite loop. Basically halting means terminating. So can we have an algorithm that will tell that the given program will halt or not.
Is it possible for an outer function to halt?
Then there would be some impossibility, i.e., a condition arises which is not possible. It is impossible for outer function to halt if its code (inner body) is in loop and also it is impossible for outer non halting function to halt even after its inner code is halting.
Which is an example of a non halting CPU?
A Turing machine is a general example of a CPU that controls all data manipulation done by a computer. Turing machine can be halting as well as non halting and it depends on algorithm and input associated with the algorithm.