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Nov 9, 2014 · There is a difference between the halting problem and the proof of its undecidability. The halting problem is just a specification for a program H H: as input the program gets the source code of a program P P and an input x x, and the program H H must return true if P P halts on input x x and false otherwise.
Gödel's incompleteness theorem and the undecidability of the halting problem both being negative results about decidability and established by diagonal arguments (and in the 1930's), so they must somehow be two ways to view the same matters. And I thought that Turing used a universal Turing machine to show that the halting problem is unsolvable.
Mar 26, 2022 · A language for which such a Turing machine exists is called semi-decidable. When a Turing machine decides a language, it halts on every input, and somehow points out whether or not it belongs to the language. A language for which such a Turing machine exists is called decidable, or recursive. Not all semi-decidable languages are decidable.
But let us assume that the human brain can solve the halting problem for Turing Machine. Then the computational model of Turing Machines becomes much less important, and the Church-Turing Hypothesis becomes much less relevant, as we have a more powerful model called the Human Model (to avoid the word machine). Of course this (arbitrarily long ...
For example, we have been unable so far to compute many values of busy beaver functions, which measure the maximal number of steps a halting Turing machine can run given the number of tape symbols and number of states. According to the Church–Turing thesis, every machine can be simulated by a Turing machine.
Jan 29, 2020 · The halting problem states that there is no Turing machine that can determine whether an arbitrary Turing machine halts on $\\epsilon$. But I try to ask something different, can we find a specific T...
Apr 1, 2020 · Halting problem for fixed Turing machine and fixed input. Ask Question Asked 4 years, 6 months ago. ...
Apr 11, 2015 · It does so by taking the input to the normal halting problem, and making a new TM that always starts with a blank tape, and writes the normal halting problem input to the tape as its first set of steps - so if this modified machine halts when starting with an empty tape, the normal halting problem input halts with whatever its input. Therefore we can't decide the blank tape halting problem.
Jul 6, 2022 · 0. Proof of concept referenced by Nathaniel tells that the idea for a contradiction resulting from assuming a decider halts halts that decides the halting problem is to construct a Turing machine g g that "does the opposite of what halts halts says g g should do, so halts(g) halts (g) can not return a truth value that is consistent with whether ...
Jul 8, 2015 · From this, I infer that the two variants of the nondeterministic halting problem are both Turing equivalent to the classical deterministic halting problem. However, I also show that each of these definitions of halting is directly related to a corresponding definition of the language recognized by a Turing machine, and this relation can be simply expressed on the condition of choosing consistent definitions.
