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Nov 20, 2019 · To understand better the halting problem, we must know Decidability, Undecidability and Turing machine, decision problems and also a theory named as Computability theory and Computational complexity theory.
The answer must be either yes or no. Proof − At first, we will assume that such a Turing machine exists to solve this problem and then we will show it is contradicting itself. We will call this Turing machine as a Halting machine that produces a ‘yes’ or ‘no’ in a finite amount of time.
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.
However, there are Turing machines which can predict the output of some other Turing machines. 3 The Halting Problem. Let's try a more modest goal: rather than actually attempting to predict output, let's just predict whether a Turing machine halts on its input, or runs forever. De nition 5.
The canonical example of a computation that is not decidable is the halting problem, which was originally proposed by Alan Turing himself.
The Three Halting (3-Halt) problem is the problem of giving a decision procedure to determine whether or not an arbitrarily chosen Turing Machine halts for an input of three strokes on an otherwise blank tape.
Can we tell if a given TM is a decider? Or, even simpler, can we tell if a given TM halts on a given input string? No, the latter is the famous Halting Problem that was shown undecidable by Alan Turing in 1936.
Turing Machines, diagonalization, the halting problem, reducibility. now, but with the addition of an in nite memory space on which it can read and write. The memory is modeled as an in nite tape of individual cells, and, in addition to the machine states that we have so .
Let P be a Turing machine that solves the halting problem. In other words, given an input machine M, P (M) accepts if M(0) halts, and rejects if M(0) instead runs forever.
Turing's proof of incomputability of halting talks vaguely about the “motion” of his machine, just as the above specification of halts may be accompanied by a statement saying that it is to be written in Pascal.
