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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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1answer
56 views

Is there a $\Sigma^0_3$ variant of the halting problem?

In terms of the arithmetical hierarchy, the halting problem is known to be $\Sigma^0_1$-complete, and the so-called universal halting problem, is the problem of determining whether a given computer ...
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171 views

Does the Linz Ĥ specify a computation that never halts when the embedded halt decider is a UTM?

When we hypothesize that the halt decider embedded in Ĥ is simply a Universal Turing Machine (UTM) does this define a computation that never halts when Ĥ is applied to its own Turing machine ...
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1answer
189 views

Halting problem undecidability and infinitely nested simulation

Halting problem: In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, ...
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1answer
37 views

Proof that R (decidable languages) is not closed under homomorphism

After searching the internet for a bit, I found that the same proof came up over and over again. The thing is, it seems like the proof is incomplete. Here's the proof: However, the recursive ...
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1answer
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Would P (simplified Linz Peter Ĥ) ever stop if simulating halt decider H never stopped simulating it?

Would P (simplified Linz Peter Ĥ) ever stop if simulating halt decider H never stopped simulating it? Same question worded concretely: Does the provided x86 execution trace of P show that P is ...
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0answers
42 views

An approximation variant of the halting problem

It always has been bugging me that we (humans) know pretty easily when most programs we write halt or not, but the halting problem is still undecidable. I have just thought of a variant approximation-...
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1answer
37 views

What is the strongest weaker version of the halts() function?

I was wondering about some questions related to the Halting problem. I might have not understood all the assumptions in it fully. Would you kindly help me, please? I understand that the construction ...
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1answer
23 views

How can we solve halting problem efficiently?

I was doing exercises regarding the halting problem and there is this question where I am stuck Ques: it goes like suppose if you can decide the halting problem with a query "Is <tm,s> ...
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1answer
53 views

Are run time bounds in P decidable when the problem is promised that an input program must halt?

I'm solving Problem 11-10(b) in "what can be computed". 11.10 Consider the decision problem HALTSINSOMEPOLY (HISP), defined as follows. The input is a program P, and the solution is “yes” ...
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1answer
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Confusion in the added loop of the Halting Problem

I know there's like a thousand questions about this topic in the site and elsewhere. I'm just going to pick one that at least for me it serves as a good basis for my question. The answer by Rick ...
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1answer
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Please help me understand this proof of the undecidability of “Do two halting Turing machines accept the same language?”

Do two halting Turing machines accept the same language? Proof that it is undecidable(credit to another user on this website: "Tom van der Zanden"): Let M be an arbitrary Turing machine. Let ...
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Is the halting problem decidable for TMs that do not write to the tape? [duplicate]

Is the halting problem decidable for TMs that do not write to the tape? Once a read only tape TM repeats a configuration, it will loop forever. Therefore, all we have to do to decide the above is ...
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Can a program exist that halts only if it can prove that it doesn't halt?

Consider a program P that enumerates possible proofs in some proof system and halts only if it finds a valid proof that P does not halt. Clearly no such proof exists, or the program would eventually ...
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1answer
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How to prove (un)decidability

Let's say we have a string s , a code size limit of b bytes and a time limit t, the question is then whether or not it is possible to construct an algorithm that prints the string within the time ...
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1answer
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Show that a language is not decidable by reducing from ATM

Let (ATM denotes the language $\{\langle M,w \rangle \mid \text{TM $M$ accepts $w$}\}$) show that the language L={<M1,M2,w> | M1 and M2 both accept or reject w} is undecidable by reducing ATM ...
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Can a Kolmogorov complexity oracle solve halting problem?

I can find https://www.nearly42.org/cstheory/halting_to_kolmogorov/ but the halting problem part is unrelated to proof that kolmogorov can't be solved(still that assume it solvable and output a longer ...
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1answer
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Given a Turing Machine $M$, if I know $L(M)$ is finite, can I solve the halting problem?

Say I'm given an oracle that tells me whether or not $L(M)$, the set of words accepted by a Turing Machine $M$, is finite. By leveraging this oracle, can I solve the halting problem? That is, on an ...
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1answer
52 views

Could the halting problem in theory be solved for any finite set of Turing Machines?

Suppose there's a program A that decides whether or not every program halts. Then we could construct program B that invokes A and does the opposite. Do I halt? If so, loop. Do I loop? If so halt. That ...
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1answer
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Issue with the Halting Problem

For clarity, I'll claim the supposed impossible program to be 'Code X'. Something doesn't seem to make sense about the proof against Code X: Consider a code that halts if you input oranges, but doesn'...
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halting problem vs watchdog

I have a theory that all finite state machines can be monitored by a second turing machine with infinite tape to determine if the state of the first machine was repeated thus reaching the conclusion ...
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2answers
55 views

State whether the language is in $R$, $RE$, etc. The intuition for the solution

I saw the solution but can't understand the intuition of the following question: Let's define $$L^{\ge k} = \{w\in L : |w| \ge k\}$$ and $$L=\{\langle M\rangle | \exists k:L(M)^{\ge k} = \overline{HP}^...
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2answers
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Proving decidability

Regarding the following languages $L_1$ and $L_2$, I want to prove that $L_1$ is decidable and $L_2$ is undecidable. I want to construct a turing machine which can decide $L_1$ and reduce the halting ...
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1answer
61 views

Why is the common explanation to the halting problem an oversimplification?

So watching many youtube channels, the explanation to the impossibility of solving the halting problen involves assuming you can, doing the opposite, and feeding it back into itself to create a ...
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1answer
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Is there a connection between the Undecidability Theorem and “software complexity”?

I was reading Complexity: The Emerging Science at the Edge of Order and Chaos and a certain passage got me really intrigued. When discussing Chris Langton's explorations of artificial life algorithms,...
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1answer
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Halting (on empty input tape) for an infinite subset of all Turing machines

As is well known, there is no single procedure for deciding whether any given Turing machine halts on an empty input tape. This is easily shown, e. g., by applying Rice's theorem. But what if, instead ...
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2answers
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Decidability of Turing machines and misconceptions on the halting problem

In an online discussion on Turing machines and decidability recently, I blatantly theorized that any problem about a specific single Turing machine must be decidable, the question of undecidability ...
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1answer
69 views

What is the actual scope of the Halting Problem impossibility result?

Consider the Halting problem : No TM H exists which given any TM and input, decides whether that TM will halt on that input. The usual proof (informally) is that if such an H existed, then a function ...
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1answer
63 views

What is the contradiction in the proof of the halting theorem?

In the standard proof of the halting theorem, you are asked to assume that a TM_0() exists that takes another TM_1() and a string W and outputs whether TM_1() halts or executes forever right on string ...
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1answer
24 views

Uncertainty of coroutines writing to single socket

A program runs in a low-spec hardware utilizes coroutines writes to a single socket but how does the socket know when the data should be sent as there could more coroutines writing given N time. I ...
4
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1answer
140 views

Kleene's Theorem and TMs

I wanted to know that based on Kleene's theorem (a language is regular iff some FSA recognizes it), does every regex have a TM (Turing machine) that halts on exactly the same language? Is this ...
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0answers
20 views

Other than correlation of events, what is the halting problem about?

Object B can be in two state 1(stopped), and 2(running) at an arbitrary time t in the future. Object A can be in two states x, and y at t0. However, if A is in state x, B must be in state 2 at t, and ...
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Can you write an algorithm that can generalize another algorithm?

Can you write an algorithm which can take in a given function/algorithm, and produce a distribution of generalizations of the function at hand? One such simple example of generalization might mean the ...
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Computability of a halting oracle for a specific class of machines

Let us consider the set of machines/algorithms with constant inputs (I would have preferred to say no inputs but I was told that every algorithm/machine has to have an input). We call $\mathcal{M}$ ...
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1answer
60 views

Existence of particular/specialized halting oracles

It is known that there does not exists an oracle $H$ which given any pair $(M,I)$ where $M$ is a machine and $I$ is an input (possibly still a machine) to have $H(M(I)) = YES$ if $M(I)$ halts and $H(M(...
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1answer
62 views

Faults in the halting problem reasoning

I find very interesting the problem of existence of a machine $H$ which given as input any algorithm $P$ outputs whether $P$ halts or not. Alan Turing disproved the existence of such an $H$ machine in ...
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1answer
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Cryptosystems whose hardness depends on solving the halting problem?

There has been a lot of work on building cryptosystems whose general security guarantees are attached to famous complexity classes. This post Gives a list of some famous cryptosystems whose underlying ...
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2answers
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Why do we proof the halting problem with turing machines?

It can be shown that Turing machines, μ-recursive functions and reasonable programming languages can compute/decide the same problems. I wonder why we then still proof the halting problem with Turing ...
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1answer
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Is Rice's Theorem equivalent to the Halting problem?

As I understand it Rice's Theorem seems to imply the existence of the Halting problem. That is, with Rice's Theorem, we can prove that the Halting problem is undecidable. However, to me, it seems like ...
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2answers
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Is the halting problem pointless?

Some programs run quickly, some programs run slowly, and some spend all eternity whirring and whizzing without ever halting. The halting problem uses a thought experiment to prove that there cannot ...
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Turing machine M' from M

Let M be a Turing machine not necessarily halting on every input. Construct Turing machine M′ which halts on w if ww ∈ L(M) and does not halt otherwise.
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1answer
67 views

Union of every language within group of decidable languages is also decidable?

So I was trying to solve following exercise: Let $(L_{i})_{i \in \mathbb{N}}$ be a family of decidable languages - this means that every $L_{i}$ is decidable. Then $\cup_{i \in \mathbb{N}}L_{i} $ is ...
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Why is it impossible to iterate over all TMs with $n$ states and $k$ symbols that halt after $m$ steps on $\epsilon$?

Define $\{\sigma(n,k,m,i)\}_{i=1}^{l_m}$ an ordered set of all TMs with $n$ states and $k$ symbols that halt after $m$ steps on $\epsilon$ There are $(2kn)^{kn}$ TMs with $n$ states and $k$ symbols, ...
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3answers
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Are files download times actually unknowable due to the halting problem?

When downloading a file from the internet to our computer we are usually prompted with an estimate of how long it will take for the file to be downloaded. From the Halting Problem, we know that $\...
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1answer
47 views

Why is the Halting problem decidable for Goto languages limited on the highest value of constants and variables?

This is taken from an old exam of my university that I am using to prepare myself for the coming exam: Given is a language $\text{Goto}_{17}^c \subseteq \text{Goto}$. This language contains exactly ...
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1answer
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Turing-completeness of Goto language with limited constants

This is taken from an old exam of my university that I am using to prepare myself for the coming exam: Given is a language $\text{Goto}_{17} \subseteq \text{Goto}$. This language includes exactly ...
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1answer
74 views

Confusion of halting problem

Show that the following problem is solvable.Given two programs with their inputs and the knowledge that exactly one of them halts, determine which halts. lets P be program that determine one of the ...
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Can you give an example of a problem in $EXP^{RE}$ but not In $P^{RE}$

Can you give an example of a problem in $EXP^{RE}$ but not In $P^{RE}$?
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3answers
64 views

Halting problem vs. automated theorem proving?

In the Theory of Computation tutorial offered by Complexity Tree (I just began the 2nd video), it talks about how the Halting problem was developed to show that mathematics could not be automated. ...
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Can a pushdown automaton solve the halting problem for another Pushdown automaton?

Can a pushdown automaton solve the halting problem for another Pushdown automaton? It's already shown here turing machine can solve the halting problem for a pushdown automaton. Decidability of ...
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1answer
246 views

What's the complexity class of determing the halting problem of a finite memory Turing machine?

What's the complexity class of determining the halting problem of a finite memory Turing machine? What is the computational complexity class of determining whether a machine halts on any input if it ...

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