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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.

445 questions
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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 find it, causing a contradiction. But that…
Silver
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Is halting problem computable for particular inputs/assumptions

From my understanding of the proof that halting problem is not computable, this problem is not computable because if we have a program P(x) which computes if the program x halts or not, we got a paradox when giving P as an input to the same P,…
ela
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Can a runtime environment detect an infinite loop?

Would it be possible for a runtime environment to detect infinite loops and subsequently stop the associated process, or would implementing such logic be equivalent to solving the halting problem? For the purpose of this question, I define an…
Kyle Strand
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Chaitin's constant is normal?

According to this source, Chaitin's constant $\Omega$ is normal. Each halting probability is a normal and transcendental real number that is not computable, which means that there is no algorithm to compute its digits. Indeed, each halting…
Anon21
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Halting Problem without self-reference: why does this argument not suffice (or does it)?

I'm trying to find a way to explain the idea of the Halting Problem proof in as accessible a manner as possible (to undergrad CS students). The simplest argument I have found is this one; this is precisely the style of treatment I am aiming for.…
badroit
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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 contain / or \ does: If the string p is a substring of r, go to step 2; otherwise…
user139273
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Can we meaningfully state for what proportion of possible programmes we can determine if they halt, do not halt, or wether it is still undetermined?

[My apologies, I am not a computer scientist, merely an interested amateur. I apologise if this question does not make sense, is a known result, or a duplicate] To quote Wikipedia: The halting problem is the problem of determining, from a…
Neil Tarrant
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The halting problem for laymen

This line from Wikipedia made me want to ask this question: There is, however, no general procedure for determining whether an expression involving looping instructions will halt, even when humans are tasked with the inspection. The theoretical…
Lance
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How strong "Consistent Guessing Problem" is?

I saw "Rosser’s Theorem via Turing machines" at: https://www.scottaaronson.com/blog/?p=710 The modified halting problem (Consistent Guessing Problem) CGP is used in the proof: CGP(M) - accepts if M accepts on a blank tape CGP(M) - rejects if M…
smrt28
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Can we prove that a time machine is impossible using the Halting Problem?

Let us take a hypothetical machine i which halts on the ith day of the month if it rains on the ith day of the month. Basically it describes the present. If we put this machine in a Halting Machine it should say whether the machine would halt. i.e.…
Souradeep Nanda
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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 clarify or correct my understanding of it. To start,…
DeveloperGuy
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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 diagonalization proof. But what happens when we…
Sid Meier
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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 a set or else a proper class, in cases where we…
erik
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Computational models where halting problem is solvable

Are there computational models that can be considered useful for solving common programming problems, where it can be proven that computation will terminate for all possible inputs?
zduny
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How big is the class of problems that can be analysed to halt with static analysis. Is this class sufficient for any practical purposes?

When the halting problem is discussed, often the counterproof consists of some unsolved mathematical problem or a self-reference. Is the halting problem decidable for pure programs on an ideal computer? Is this of any relevance for most programms…
HopefullyHelpful
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