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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Can we find a Turing machine such that there is no Turing machine to decide whether it halts on $\epsilon$?

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 ...
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Are non halting programs not computable?

Are non halting programs not computable? How are these two sets of programs related: is a non halting program just a specific example of a type of program that is not computable or is it technically ...
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Union of halting-like problem and non-halting-like problem

I came across the following problem: Define languages $L_0$ and $L_1$ as follows : $L_0=\{⟨M,w,0⟩∣M\text{ halts on }w\}$ $L_1=\{⟨M,w,1⟩∣M\text{ does not halt on }w\}$ Here $⟨M,w,i⟩$ is ...
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how is the set of undecidable programs related to the set of non-halting programs?

Is there a non-halting program for every undecidable program? is undecidable the "same thing" as non-halting? Thanks!
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Undecidability of two Turing machines acting the same way on an input

So I need to find a reduction to the (undecidable) problem of deciding if two Turing machines $M_1$ and $M_2$ behave the same way on an input $x$. "Behaving the same way" is defined like this: $M_1$ ...
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In the reduction from HALT to ALLHALT, why does the constructed Turing machine loop indefinitely when the inputted Turing machine rejects?

Let HALT be the language $\{\langle M, w\rangle : M\text{ is a TM that halts on }w \}$. Let ALLHALT be the language $\{\langle M\rangle : M\text{ is a TM that halts on all inputs}\}$. Use a reduction ...
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Proving Problems are Undecidable/ Semi decidable? E.g. Halting Problem, Membership Problem? [duplicate]

I am having issues finding similarities in different cases where a problem such as the Halting Problem or the Accept-Λ problem is reduced to the Membership problem to prove that it is semi-decidable ...
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TM1 accepts w1 vs TM1 halts on w1

What is difference between following two problems, their decidability and recognizability status: Given Turing Machine TM "accepts" given string w. Given Turing Machine TM "halts on" given string w. ...
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is the empty language L = ∅ a subset of every languages?

I need to show false the following claim Every language L which is a subset of $A_{TM}$ ($L \subseteq A_{TM}$) is undecidable. For this, I wish to use the empty language L = ∅ (I know is decidable)...
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if A is decidable then B is decidable too

Assume that a language A is reducible to language B. The claim is true? if A is decidable then B is decidable too. The correct answer is: This claim is wrong. If A is e.g. the empty language (...
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Is checking if the length of a C program that can generate a string is less than a given number decidable?

I was given this question: Komplexity(S) is the length of the smallest C program that generates the string S as an output. Is the question "Komplexity(S) < K" decidable? With respect to ...
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Are there any problems that reduce to the halting problem?

I'm reading through sipser and there is a lot of computability problems that the halting problem reduces to, i.e. if $A_{TM} = \{\langle M,w\rangle : M$ accepts input $w\}$ then $A_{TM} \leq P$ where ...
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Turing recognizable but not Turing decidable language cannot have TM do not halt on infinitely many inputs

Sorry, I think I misunderstand the question, It should read as if $L$ is turing-recognizable but not decidable, then there exists infinitely many input that any TM will not halt on it...
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How can Turing complete machines exist theoretically if the halting problem is undecidable

As the question says, if I input on the tape of a Turing complete machine a program that solves the halting problem with the correct inputs the program will never end its execution regardless of ...
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On the computable function of a problem that halts

Let's say program $P$ with given input $i$ is found to halt (or doesn’t halt) by a Turing machine. Is it true that the same program $P$ with input $F(i)$ also halts (or not, respectively), where $F$ ...
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Why do intuitionists accept the nonconstructive proof that the halting problem is undecidable? [duplicate]

On the intuitionism page at Stanford Encyclopedia of Philosophy (SEP), it's said in Section 3.3 that Because of the finiteness of a natural number in contrast to, for example, a real number, many ...
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Concise Way To Specify The Space Of All Python Programs Under A Certain Size And Running Time?

Given the grammar of the Python language, is there a concise way to specify the space of all possible (and correct) Python programs? To avoid the underlying halting problem, the specification would ...
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How to write a coterminating, effectful program?

[Using Idris for code examples and terminology, but the question is not about Idris per se] In a post titled A Neighborhood of Infinity, @sigfpe argues that "the kind of open-ended loop we see in ...
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I want to know where there is the flaw in my argument

I came across following problem to finding whether the following language is decidable or semi-decidable or not even a semi-decidable. $L: \{\langle M\rangle: M\space is\space a\space TM\space and\...
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Why is it not possible to prove that two Turing Machines calculate the same function?

I was wondering why it is not possible. Is it because the corresponding language is not decidable, or because of the fact that it is not guaranteed that a Turing machine halts on every input?
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Busy-Beaver-like question for WHILE-Programs (Theoretical CS)

So this is exam-task is called "Busy WHILE-Programs" In our lecture it was proven that WHILE-Programs are turing-complete. In short a WHILE-Program only allows the following: ...
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Proof by reduction and Turing machines [closed]

This is a practice question I have, but I can't wrap my head around it. ............. Let L = {M | M is a TM that halts with exactly two words on its tape in the form Bw1Bw2B}. B = Blank Position the ...
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What Makes A TM undecidable (using Recursion Theorem)

PROOF :We assume that Turing machine H decides ATM for the purpose of obtaining a contradiction. We construct the following machine B. B =“On input w: Obtain, via the recursion theorem, ...
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Given we restrict the time and memory allowed what bounds can we place on a halting decider?

If a program is given as much memory and as much time to execute as it wants, then the halting problem is undecidable, and by Rice's theroem all non-trivial, semantic properties of programs like that ...
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Since the halting problem is undecidable, does that mean that there exists an always undecidable program?

The usual demonstration of the halting problem's undecidability involves positing an adversarial machine (call it $A_0$) that runs the decider machine (call it $D_0$) on itself and performs the ...
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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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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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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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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 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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Does solving all Halting problem instances 'in the limit' imply we solve an undecidable problem?

The recent Arxiv paper "Learning the undecidable from networked systems" attempts to construct a network of $N$ Turing machines$^1$ that can solve the Halting problem for any program of size $O(\log N)...
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Enumerate over all halting Turing Machines?

I understand that it is possible to enumerate over all Turing Machines. My understanding of how this works is by fixing an encoding of natural numbers to TM descriptions, and then enumerating the ...
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Counter Machine (Halting Problem)

How can we show that Halting Problem for one-counter additive machines is decidable ?
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Halting Problem, Typed Version: A Headache

After many years, I have been revisiting the venerable old Halting Problem and the self-referential / diagonalization “party trick” that shows that there is no Turing Machine able to solve it. I was ...
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Would Schmidhuber's theories of everything be capable of performing hypercomputation?

Jürgen Schmidhuber pointed out that a simple explanation of the universe would be a Turing machine analogy programmed to execute all possible programs computing all possible histories for all types of ...
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Is determining if a Turing machine runs in constant time decidable if one assumes it halts?

As the title states, is determining if a Turing machine runs in constant time decidable if one assumes it halts? The decision problem, more formally: Given a Turing machine $M$ where it is assumed ...
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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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Why a TM with infinite states can decide the halting problem?

Assuming we have a model of TM with an infinite number of states. The domain and range of the transition function are also infinite. Given a description of a TM $M$ and a string $w$ how can we use the ...
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How to create model for a powerful language whose programs are guaranteed to terminate?

I'm creating a powerful regular expression matching system that can be augmented by adding small microprograms to deterministic finite automaton (DFA) states. The microprogram solves the big bang ...
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Recognizer for decidable language and words it doesn't halt on

Suppose we have a decidable language B (there exists some TM that decides it). Suppose we have another TM M which only ...
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201 views

How to prove that a problem is undecidable by using the Halting problem?

I cannot understand how to reduce the halting problem to a property to show that is undecidable. For example, I have this property of a Turing Machine and I have to prove if it's recursive or not: "...

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