# Questions tagged [halting-problem]

Questions concerning the Halting problem which is to decide whether a given a program halts on a given input.

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### $L = \{ \langle M \rangle \mid M$ is a Turing machine and $\mathcal{L}(M)$ is decidable $\}$

$L = \langle M \rangle \mid M$ is a Turing machine and $\mathcal{L}(M)$ is decidable $\}$. How could I show this language is undecidable using the HALTing method? A language $L$ is undecidable if its ...
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### Variations of the halting problem

Let $M$ be an arbitrary Turing machine and $w \in \{0, 1\}^{*}$ be a binary string. The language $\text{HALT} = \{\langle M, w \rangle : M ~\text{halts on input} ~w \}$ is undecidable by the famous ...
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### The Halting problem proof is wrong?

First, let's see the pseudocode proof of halting problem: P(x) = run H(x, x) if H(x, x) answers "yes" loop forever else halt Then we have a ...
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### Probabilistic halting problem

I'm a physics and math student working through Nielsen & Chuang's text on quantum computation and information. I don't have much experience in CS theory, so some of these exercises are confusing ...
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### Why, really, is the Halting Problem so important?

I don't understand why the Halting Problem is so often used to dismiss the possibility of determining whether a program halts. The Wikipedia [article][1] correctly explains that a deterministic ...
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### Can we enumerate finite sequences which have no halting continuation?

Note: this question has been cross-posted to Math.SE, after about a week here. I am trying to deepen my understanding of the relationship between the Halting Problem and Godel's Completeness Theorem (...
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### Halting problem in C++

The halting problem relies on the fluidity of Turing machines. That is, a string can represent a machine. Can you do the same for C++ on a modern computer? Let's see my first attempt. Let ...
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### How to prove the language of Turing machines that run at most $4|x|^2$ steps is not recursive?

I am trying to prove that the language $$L=\{M\mid M\text{ is a TM and for all }x\in \Sigma^*\text{ with }|x|>2, M\text{ on }x\text{ runs at most }4|x|^2\text{ steps}\}$$ belongs to Co-RE but ...
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### Is halts-if-valid decideable?

I have a suspicion that Turing's famous proof that the halting problem is undecidable may not prove exactly what people assume that it proves. It may only prove that it is possible to limit the ...
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### Reduction to proof undecidability of the problem: machine M and N accept infinitely many words

I am struggling with the following problem: Decide whether this problem is decidable or not: For two given Turing Machines M and N, there exists infinitely many words accepted by both machine M and ...
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### How can I write a genetic programming algorithm, given that the Halting problem is unsolvable?

I am learning genetic programming and to practice I want to write a simple algorithm which evolves a program that solves a simple function (say, square root). I intend to represent programs as ...
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### Is Halting problem only applicable to infinite languages

Is the halting problem, only applicable for infinite languages? I assume that if the language is finite, then we can search over all words?
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### Can every Turing Machine be translated into a SAT formula?

For the proof of "Cook-Levin Theorem", for a Turing Machine $M$ that accepts a language $L \in NP$ and input $x \in \{0,1\}^*$, we can create a SAT Formula, that is satisfiable if and only if $M$ ...
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### Is the halting problem solvable for NPDAs?

After the total silence in response to my last question, I am rethinking my assumptions. DPDAs are, of course, solvable, and I believe that their loops can be found in the manner I described in my ...
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### Show that the following language is undecidable

$\{ M \mid M \text{ is a machine that runs in }100n^3 + 300\text{ time }\}$ I am currently stuck with this one. I thought of reducing HALT to M as the reduction seems legitimate to me: if the first ...
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### Computability: Proving a predicate is not recursively enumerable

Let P(p) <=> for each x, comp(p,x) is defined. Can anyone explain to me how to prove that P is not RE (recursively enumerable) ?
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### Detecting loops in NPDAs

I'm aware that the halting problem is solvable for PDAs, but I have recently discovered that I am wrong about how to actually do it. I used to think that you could detect an infinite loop by meeting ...
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### Define the following problem as a language and prove that it is undecidable with a reduction from the halting problem.

...Knowing whether a Turing machine will ever output your name on the tape. The language is the set of all TMs that print your name. Reduce from HALT TM. I had this problem on my exam. From my ...
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### Why is the halting problem decidable for LBA?

I have read in Wikipedia and some other texts that The halting problem is [...] decidable for linear bounded automata (LBAs) [and] deterministic machines with finite memory. But earlier it is ...
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### Prove if a property of a Turing Machine is decidable or not, how can I do it?

I cannot understand how to prove if a certain property of a Turing Machine M is decidable or not. For example, if a have this: (1.1) "M always halts within 100 steps" or this (1.2) "M recognizes ...
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### Is there an impossibility to mechanically distinguish between sets and classes?

Assuming only computable functions, and in line with set theory, defining a "proper class" as a collection that is itself not allowed to be a member of a set. A "collection" is then defined as either ...