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Nov 20, 2019 · 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. Now, lets discuss Halting problem: The Halting problem – Given a program/algorithm will ever halt or not?
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.
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.
Suppose there is an algorithm, and therefore, a Turing machine, H H, that takes an encoding of another \text {TM} TM, M M, as input, along with an arbitrary string, w w, and always halts, accepting if M M will halt when processing w w as input, and rejecting if it will not halt on w w.
17.1 The Halting Problem Consider the HALTING PROBLEM (HALT TM): Given a TM M and w, does M halt on input w? Theorem 17.1 HALT TM is undecidable. Proof: Suppose HALT TM =fhM;wi: M halts on wgwere decided by some TM H. Then we could use H to decide A TM as follows. On input hM;wi,
Turing Machines, diagonalization, the halting problem, reducibility 1 Turing Machines A Turing machine is a state machine, similar to the ones we have seen until now, but with the addition of an in nite memory space on which it can read and write. The memory is modeled as
The halting problem asks whether a given program P will halt (i.e., complete execution and return a result after a finite number of steps) when run on a given input, x. The halting problem is undecidable.
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. Here P (M) means P run with an encoding of M on its input tape, and M(0) means. M run with all 0’s on its input tape.
