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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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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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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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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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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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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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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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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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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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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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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Is it possible to construct a Turing Submachine such that a regular turing machine can decide whether the TSM halts but the TSM cannot [closed]

Is it possible to construct a not fully turing complete version of a turing machine such that a regular turing machine can solve the halting problem for the Turing Submachine but the Turing Submachine ...
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Semi-decidability of the language $\overline{L_{\epsilon}}$

Firstly consider the problem: given $L_H = \{R(M)w : M \in TM_0, w\in L(M)\}$ where $R(M)$ are encoded transitions of $M \in TM_0$. Assume for contradiction $\overline{L_{H}}$ is semi-decidable, then ...
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Do there exist coding languages where the halting problem is solvable but not trivial

Does there exist a coding language where 1. It is always possible to determine whether a computer program will halt or run forever. And 2. The answer is not always yes. (or always no) So languages ...
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Under what kind of oracles are $P$ and $NP$ equivalent?

How strong have the oracles needed to be for these two classes to be proven equivalent with respect to them? For instance: is $P^H$ = $NP^H$ (ie. is $P$ equipped with an oracle to solve the halting ...
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If a turing machine can't solve the halting problem for a machine X, does this imply that X is at least as powerful as a turing machine?

Say I have a deterministic machine X, and I prove that a turing machine can't solve the halting problem for this machine when given a certain input. Does this imply that this machine X is turing-...
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proving $E_{TM}$ is undecidable using the halting language

How to prove that: $E_{TM} = \{\langle M\rangle\mid M \ is\ a\ TM\ and\ L(M)=\emptyset\}\notin R$ (is undecidable) using the language: $H_{halt}=\{(⟨M⟩,w):M\ halts\ on\ w\}$. I tried to prove by ...
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Is the undecidability of a given problem undecidable?

Given an input problem P, can you construct an algorithm A to compute whether or not P is decidable or undecidable? In other words, is the undecidabiliy of a problem undecidable? My initial guess is ...
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How to build a TM which decides $L_k := \{(\langle M \rangle ,x)\in HP : |(\langle M \rangle ,x)| \le k \}$

For a specific natural $k$ we define the language of couples $(\langle M \rangle, x)$ such that $M$ stops on $x$ and the couple's encoding is bounded by $k$ i.e $L_k := \{(\langle M \rangle ,x)\in HP :...
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Halting problem theory vs. practice

It is often asserted that the halting problem is undecidable. And proving it is indeed trivial. But that only applies to an arbitrary program. Has there been any study regarding classes of programs ...
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Zero-Sum Games and Halting Problem

Wikipedia states on the page of the halting problem, "For any program f that might determine if programs halt, a "pathological" program g called with an input can pass its own source and its input to ...
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Can a halting configurations of a Turing Machine has the same state of another configuration has?

At first, I believed since the state a halting configuration is at will be a halting state, whenever a configuration goes into that state, the TM halts. Hence, there should not exist two ...
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How could you “solve” the halting problem if, hypothetically, the busy beaver numbers were “small”?

I read that if BB(n) did not grow faster than all computable sequences of integers, you could solve the halting problem and contradict Turing's theorem. I'm trying to figure out how you could ...
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Given an input and a program when can you derive the output faster than just running the program?

Given an input string W, a description of a turning machine M, and a target output string O (W,M,O) as input, when can a machine M' decide, in fewer steps than simply running M on W, if running M on W,...

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