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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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What is the complement of Halting Problem?

I understand that Halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running or continue to run forever. ...
Pepper's user avatar
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3 votes
1 answer
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A Turing machine for which it is impossible to predict whether it halts or not on a fixed input

The halting problem is undecidable, i.e. $\not \exists$ $M$ Turing machine s.t. for every $(M_0,w_0)$ input where $M$ is the description of a Turing machine and $w_0$ is an input word, the output of $...
Heisenberg's user avatar
3 votes
1 answer
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Blank tape halting problem vs. Emptiness problem ($H_0$ vs. $E_{TM}$)

I have difficulties to differentiate the $H_0$ from the $E_{TM}$ problem. What exactly means $L(M)= \emptyset $? Is it dffierent from $input~ \varepsilon$ or is $L(M)= \emptyset \leftrightarrow input~...
chrisber's user avatar
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3 votes
1 answer
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The proportion of halting programs vs non-halting programs, of decidable programs vs undecidable languages

Can the following two statistics be bounded: the proportion of halting programs vs non-halting programs the proportion of decidable vs undecidable languages For example, can we say that one class is ...
user13675's user avatar
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2 votes
4 answers
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Misunderstanding Turing's Halting-Problem Argument

I just watched a video by Computerphile on the halting problem (https://www.youtube.com/watch?v=macM_MtS_w4) . I’m having some difficulty understanding the argument as it is made. Let me explain it ...
Israel's user avatar
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2 votes
2 answers
127 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}^...
ChaosPredictor's user avatar
2 votes
1 answer
847 views

Halting problem for fixed Turing machine and fixed input

It is known that the halting problem is undecidable even when we fix either the Turing machine $M$ or the input $w$. What if we fixed both the machine and the input? I.e., is it decidable for every ...
Heisenberg's user avatar
1 vote
4 answers
2k views

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 ...
Anonemous's user avatar
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1 vote
1 answer
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Turing machines: can a machine write to a finite number of memory cells, but not halt?

I am trying to reduce the Halting problem to show another problem is undecidable. The problem involves a program that is true if a machine $M$ writes to an arbitrary amount of memory, and false if it ...
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1 vote
2 answers
2k views

Is the halting problem decidable by an "infinite Turing machine"?

It has been shown of course that the halting problem is undecidable. That is, we cannot formulate a Turing machine that will decide for any arbitrary turing machine whether it will halt or not. ...
user56834's user avatar
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Does a DPDA halt on all inputs?

Given a deterministic DPA, is it possible to tell whether it halts on all possible inputs? Is this problem decidable? The standard halting problem is "Given a DPDA and an input $x$, determine ...
D.W.'s user avatar
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Do proofs of $HALT$'s undecidability make it clear that it's practically relevant?

The proof of $HALT$'s undecidability usually goes like this: we assume the existence of a halting decider and incorporate it into a machine $D$ that takes a TM as input, runs it on its own encoding ...
CuriosityScream's user avatar
0 votes
1 answer
243 views

Constructing a Turing machine which decides whether a fixed TM will halt on a fixed input or not

It is known that the halting problem is decidable for every fixed $M_0$ Turing machine and every fixed $w_0$ input. My related question would be the following: is it true that for every fixed $M_0$ ...
Heisenberg's user avatar
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1 answer
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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!
DeeDee's user avatar
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-1 votes
1 answer
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Halting problem. Decider “recognising itself” in the input?

This is about the halting problem. My questions are: where do you think are logical flaws in what I am going to write? How do you think this does not invalidate the proof for the undecidability of the ...
user's user avatar
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-3 votes
1 answer
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Is there an unsound solution to the halting problem that makes the following functions computable?

I'm interested in this functions \begin{align*} g(m) &= \begin{cases} \text{defined} & \text{if turing machine $m$ computes $g$} \\ \text{defined} & \text{if turing machine $...
raoof's user avatar
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