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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halting turing machine which never hang(HTM)$<$ Recursive [closed]

We know that TM with no write option have less power than standard turing machine. My teacher said that: $1.$halting turing machine which never hang(HTM)$<$ Recursive $2.$linear-bounded automaton (...
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Why REC languages is undecidable under emptiness and finiteness?

Membership problem of Recursive languages are decidable. My approach: Let $L$ be a recursive language and $M$ be the Turing Machine that accepts it. For string $w,$ if $w ∈ L,$ then $M$ halts in ...
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Number of inputs in undecidability proof of halting problem

So first, just to make sure that I understand the proof, here is the proof as I understand it: Take a program $H(x,y)$, which determines whether $x(y)$ will halt or not halt: if $x(y)$ halts then $H$ ...
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What does it mean for an integer to belong to the halting problem?

I have come across the description of a function $F: \mathbb{N} \to \mathbb{N}$ where the function is defined one way for $n \in \mathcal{H}$ and another way for $n \notin \mathcal{H}.$ In this ...
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Halting Problem - Arguments to Halting Checker Function

I'm trying to understand the Halting Problem. All the explanations I've seen state that the problem arises when passing a program to a halting check function along with itself as input. For example <...
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How to reduce $\overline{K} \leq L$, or how to show semi-decidability of a given language?

I'm currently preparing for an exam and I'm having trouble to solve the following Questions. Let $w \in \{0,1\}^*$ and let $L$ be a language defined as follows $$L = \{w \mid \mathsf{time}_{M_w}(x) \...
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Where is the error in this logic for halting Turing machines?

Let $\mathbb{H}$ be the set of all Turing machines that halt on all inputs. Consider the following Turing machine $T$. On input $\langle S \rangle$ where $S \in \mathbb{H}$ (note that the angle ...
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Question about the proof of the undecidability of the Halting Problem

From what I can see, the proof of the undecidability of the Halting Problem relies on a fairly basic self-referential paradox, the simplified version being (from Wikipedia): ...
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What is the original input for the halting question

I was reading about the halting problem recently, but I couldn't quite figure something out. We take $H(x,y)$ to be a program which works out if program $x$ with input $y$ halts, and $H_2(x,y)$ to be ...
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Help Understanding the Halting Problem

There are certain points about the halting problem that do not make sense to me. I couldn't seem to find a good breakdown of it that addresses my notes below. I was wondering if someone could ...
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Is this solution for the Turing's "halting" problem correct?

I think that Alan Turing's solution for the "halting" problem might be wrong. Turing's main premise is wrong, he assumed the only way to check whether a program halts is to run it. He didn't ...
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Is halting problem for /// solvable assuming programs that maches the regex "^/[ab]*/[ab]*/[ab]*$"?

/// is an esoteric language, and I thought of posting a code-golf problem related to it. A /// program of the form /p/q/r where p, q, and r are strings that do not ...
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Oracle for LBA halting on some input

Assume we have an oracle that tells, given a linear bounded automaton, if there exists an input on which it halts. Can we then solve the real halting problem (i.e. decide if a given Turing machine ...
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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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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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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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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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Does H correctly decide that P never halts?

Does H correctly decide that P never halts? (The C/x86 source-code for P is provided below) Halting problem undecidability and infinitely nested simulation The x86utm operating system was created so ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...
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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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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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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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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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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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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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