Questions tagged [halting-problem]

Questions concerning the Halting problem which is to decide whether a given a program halts on a given input.

Filter by
Sorted by
Tagged with
-3 votes
1 answer
67 views

Can a decider return "Undecidable" on the Halting Problem? [closed]

So, I know there is no general algorithm for the halting problem, but I was curious if a three output decider could at least give us "an" output {0 if doesn't halt, 1 if halts, U if ...
Daniel Stilman's user avatar
0 votes
2 answers
51 views

Why there can't be two instances of a "reverse" program in the Halting problem?

So in the halting problem, there is a program that reverses the output of a program that tells if the input program halts or runs forever(I'll call it the main program further). The whole paradox is ...
YKY's user avatar
  • 101
-5 votes
2 answers
69 views

Halting Problem Question

Let HALT be a program that can decide the halting problem for any program and its input. HALT has two inputs, the program and the program's input. Let OPPOSITE be a program that accepts a program as ...
StackUser20004's user avatar
1 vote
4 answers
3k views

Can we ever achieve Turing completeness?

I want to relate Turing completeness to the Halting Problem. As far as I know we say something is turing complete (eg: a programming language) when it can compute any function and can do any task. But ...
D Star Let's Explore's user avatar
-4 votes
2 answers
44 views

Proof of halting problem

if we change the halts to do_not_halt() function, it works, so how can this be a proof? def g(): if halts(g): loop_forever() if we change the halts to ...
user279163's user avatar
0 votes
2 answers
51 views

Infinite Recursion as the Intuitive Foundation for the Halting Undecidability Proof

all, I was wondering if my intuitive understanding of why the halting problem is undecidable is actually correct? TLDR: Halting problem is undecidable because it leads to infinite recursion and never ...
boinka's user avatar
  • 1
-2 votes
4 answers
96 views

Can halting problem solved by soft computation?

As far as I know, the halting problem means we can't create a program that checks whether another program is stuck or halt based on given input. This means, the program expects two inputs and one ...
Muhammad Ikhwan Perwira's user avatar
0 votes
0 answers
21 views

Reduce A ∶= {x ∈ N ∣ x < 10} to Halting Problem on empty tape

I am preparing for an exam in computability and still learning about the idea of reductions. I found an interesting problem to start with and am curious if my approach is correct: Let H0 be the ...
dport's user avatar
  • 1
0 votes
2 answers
63 views

Does exist an algorithm that decides whether a program halts or not as its timeout approaches to infinity?

By an algorithm $A(p, t)$ attempting to decide whether the program $p$ halts or not by running the program for $t$ seconds (the timeout) and trying to prove that it doesn't halt at the same time, can ...
sbh's user avatar
  • 11
3 votes
0 answers
179 views

Does this paper by Patrick Cousot describe an undecidable method for model checking?

All of the discussion is in the context of this paper. I think that the whole procedure that the paper describes is not decidable, because if we can have an algorithm for it, then we can solve halting ...
Senmorta's user avatar
0 votes
1 answer
42 views

Reduction from a language with unknown decidability to HALT

We were taught to use reductions in order to show that a given L is undecidable. My question is, given some definition of a new L, is there a way to find a reduction $$ L\leq_mHALT $$ So that I can ...
John's user avatar
  • 1
-2 votes
2 answers
106 views

Can we tell if we can tell if an algorithm halts or not?

We proved that, there exist no algorithm so it can tell us if an algorithm halts or not (a.k.a. the halting problem is undecidable). But it surely can handle some of those; can we tell which of those ...
sbh's user avatar
  • 11
0 votes
0 answers
47 views

Is game of life an example to halting problem?

I am working on a solution that can say if an initial composition is going to live forever or eventually die without calculating each generation until it reaches a stable or an ever-repeating cycle in ...
Yağız Alp Ersoy's user avatar
1 vote
0 answers
35 views

How much is decidability compromised within this restriction of the fixpoint combinator?

Though purely functional programming languages, such as Haskell, is commonly thought to have no side-effects, there is a caveat: Recursive calls may hang. I considered this to be undesirable, and ...
Dannyu NDos's user avatar
1 vote
1 answer
62 views

Is the problem of Proper Subset of decidable languages decidable?

Given 2 recursive - decidable languages $L_1$ and $L_2$ is the problem $L_1 \subset L_2$ solvable - decidable? Since both $L_1$ and $L_2$ are recursive - decidable there exist Turing Machines say $M_1$...
RookieCookie's user avatar
7 votes
1 answer
1k views

What is the complexity of theorem proving?

I'm learning some computer science and mathematics by myself. I know that proving theorems in ZFC is undecidable in general, but, is there a formal way to express how complex it is? Is it as complex ...
Otakar Molnár López's user avatar
1 vote
1 answer
30 views

Concrete example of a set with a lower degree of unsolvability

Post's problem, posed in 1944 by Post, was to know if there is a recursively enumerable set, which, being undecidable, was not equivalent to the Halting problem under Turing reducibility. While I've ...
user6767509's user avatar
0 votes
1 answer
65 views

How is there a paradox in the halting problem when you can trace it and it's very clearly non-halting?

Here's Alan Turing's halting problem in pseudocode: ...
Curious cat's user avatar
1 vote
3 answers
145 views

Halting problem unsolvability leads to a contradiction - where's the mistake?

You are all familiar with the halting problem so I won't repeat it. Suppose $H$ is a Turing machine which takes as input an encoding of another Turing machine $M$, then searches all possible proof ...
user253751's user avatar
  • 1,685
0 votes
1 answer
196 views

Modify Turing’s proof of the undecidability of the halting problem

Modify Turing’s proof of the undecidability of the halting problem to show there is no Turing machine P with the following two properties: For all Turing machines M, if M() accepts then P(⟨M⟩) ...
staz6's user avatar
  • 25
0 votes
1 answer
42 views

Is there a maximal set of programs that terminate?

It seems useful to characterize terminating programs. While trying to formulate that as a well-defined question I was wondering about the following problem: Is there a maximal decidable set of ...
timgo's user avatar
  • 103
0 votes
1 answer
70 views

Using undecidability to prove P != NP

Given the challenge of proving algorithmic bounds on the likes of 3-SAT to resolve P versus NP, I wondered whether it might be possible to use undecidability within an NP problem to ensure that we can ...
Brian's user avatar
  • 1
0 votes
0 answers
53 views

Reduction from Diophantine Equation Problem to Halting Problem

I want to study the reduction from the Diophantine Equation Problem (Hilbert's tenth problem) to the Halting problem. Can you either explain it to me or give me a credible source from which I can ...
Mgh's user avatar
  • 1
11 votes
3 answers
3k views

Detecting if three Turing Machines halt given a magic oracle that is only used twice

We were given a question in class as follows: You have a "magic oracle" that can decide if a Turing Machine halts. You have three TMs $T_1, T_2, T_3$. Device an algorithm that decides which ...
lombardo2's user avatar
  • 121
0 votes
0 answers
56 views

Is there a good example of computing a sequence that illustrates the Halting Problem?

I know that Busy Beaver problem can be used to illustrate the Halting Problem and it's probably the canonical problem used when talking about the Halting Problme . But long time ago I came across some ...
RubenLaguna's user avatar
0 votes
1 answer
59 views

Is a problem in NP if it runs in P time on a NDTM, verifiable in P on a DTM, but solution doesn’t halt on a DTM?

Say there was a decision problem which was solved optimally in polynomial time on a non-deterministic Turing machine, and verifiable in polynomial time on a deterministic TM, but would not halt when ...
J Jackson's user avatar
-3 votes
1 answer
82 views

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
  • 75
1 vote
1 answer
77 views

Efficiency of Halting Problem on finite space TMs

This question is about the (Edit: universal) Halting Problem on a TM with finite space. The Halting Problem is obviously decidable on those TMs. So my question now is how efficient we can decide it. ...
Ondolin's user avatar
  • 119
-4 votes
1 answer
83 views

can you write a halting decider that is only wrong about itself by avoiding diagonalization?

in here they claim: "there is an algorithm deciding almost all instances of [halting problem]" so I'm wonder whether there is a computable function $h':\mathbb{N}\to\{0,1\}$ such that the ...
raoof's user avatar
  • 75
-4 votes
1 answer
87 views

can you find an algorithm for this function?

consider the following function $$ \begin{align*} f(m,n) &= \begin{cases} k & \text{if program $m$ halts on input $n$ after $k$ steps} \\ m & \text{if program $m$ loops on ...
raoof's user avatar
  • 75
-2 votes
2 answers
217 views

Halting problem disproof

Introduction This is a heavily updated question I have asked on this forum previously. I have understood and corrected the earlier errors and mistakes I made, and after doing that it still seems I ...
Mercury's user avatar
  • 107
0 votes
1 answer
305 views

Does the halting problem belong to NP class of problems?

On the one hand it does not belong to NP problems because it simply is not solvable and is undecidable and on the other hand it is an NP problem because there are claims that it is NP-hard and ...
Anna's user avatar
  • 1
0 votes
0 answers
164 views

Halting problem reduction to single digit numbers

I'm thinking of the solution for severaly days, but I'm not sure about my solution is on the correct way. I need to prove that the next problem is undecidable: Input: An N program which requires an y ...
oppalarit97's user avatar
1 vote
1 answer
51 views

Is it possible to determine if a 0-arity function [a program with no input] will always terminate

The halting problem concerns programs which take input. By framing the halting problem on the diagonal argument it is clear why this is so. What about programs with no input, constant functions. Can ...
RFV's user avatar
  • 141
0 votes
2 answers
94 views

Are there some programs for which the only proof of termination, is running of the program, and waiting to see if it stops, no matter how long?

The halting problem is semi-decidable, which means that if a program terminates then it will always be able to be determined. Some programs can be proven to terminate without running them, with say: ...
RFV's user avatar
  • 141
1 vote
2 answers
87 views

Consequences of the Halting Problem

The halting problem is semi-decidable. Does that mean that: If a program terminates it can always be established/determined? If a program does not terminate It can sometimes be established/...
RFV's user avatar
  • 141
-4 votes
5 answers
397 views

Halting problem logic must be wrong

I think that I have found an issue with the proof of the halting problem, which would cause the entire proof to be invalid. To ensure I understand, here is Turing's proof of the halting problem being ...
Mercury's user avatar
  • 107
0 votes
1 answer
226 views

Are these functions computable?

consider $g$ and $f$ and $h$ as $ \begin{align*} g(m) &= \begin{cases} 1 & if\;program\;m\;halts\;on\;input\;m \\ 0 & otherwise \\ \end{cases} \end{align*} $ $ \begin{...
raoof's user avatar
  • 75
-4 votes
1 answer
411 views

Can you find a counter example for this sketch of a solution to the halting problem?

if we define halting problem as follows $ \begin{align*} h(m,n) &= \begin{cases} 1 & \text{if program $m$ halts on input $n$} \\ 0 & \text{otherwise} \\ \end{cases} \end{...
raoof's user avatar
  • 75
0 votes
0 answers
107 views

proof that halting problem is undecidable

In the book Formal languages and automata by Peter Linz, 4th edition (Jones & Bartlett Learning), on pages 300-301, there is a proof for the fact that the halting problem is undecidable. The proof ...
Ronald's user avatar
  • 89
1 vote
0 answers
38 views

Understanding unprovable halting, model theory, and (in)completeness

I know computability, but not model theory and logic, so this question may be naive or confused in that respect. A blog post of Scott Aaronson mentions a Turing Machine $M^*$ such that the statement P:...
usul's user avatar
  • 4,099
1 vote
1 answer
156 views

prove that there does not exist a Turing machine with a particular property

Prove that there does not exist a Turing machine M such that for every Turing machine K that halts on all inputs, $M$ accepts $\langle K\rangle$ if and only if $L(K)$ is infinite. The above question ...
Fred Jefferson's user avatar
0 votes
2 answers
66 views

Why is $\{ w \in \Sigma^* : M_w[\epsilon]\downarrow \land |w| \leq 7\}$ decidable?

I get that the argument for this set $\{ w \in \Sigma^* : M_w[\epsilon]\downarrow \land |w| \leq 7\}$ to be decidable is that $|w|\leq7$ meaning it is a finite set and therefore it can be decided. ...
linuxxx's user avatar
0 votes
0 answers
59 views

How should I imagine $M_w[\epsilon]\downarrow$ for the empty halting problem or $M_w[w]\downarrow$

I'm learning about computability problems e.g. reducing the general halting problem to the halting problem on a blank tape. But before I can understand this problem I first have to understand what ...
linuxxx's user avatar
0 votes
1 answer
237 views

Is the set of Turing machines that halt on infinitely many inputs not recursively enumerable?

Consider this "generalized halting problem": $$ GHP = \{<M>| \mbox{ there are infinitely many inputs that $M$ halts on}\}. $$ I'd like to prove that $GHP\notin RE$, but it doesn't seem ...
N O's user avatar
  • 3
0 votes
0 answers
35 views

Is this version of the halting problem NONELEMENTARY?

Input: A TM $M$ and an integer $k$. Output: Yes if $M$ halts within $2\uparrow\uparrow k$ steps (where $\uparrow\uparrow$ is tetration (iterated exponentiation)). Intuitively, it seems like this has ...
N O's user avatar
  • 1
1 vote
1 answer
118 views

a halting turing machine

Prove that there does not exist a universal Turing machine that takes a pair $\langle M, w\rangle$ as input, where M is a Turing machine and w is a string, and that always halts, accepts if $M$ ...
Fred Jefferson's user avatar
0 votes
1 answer
121 views

Is there a Turing machine that packs a machine and its input into a single machine?

Let $U$ be the universal Turing machine. Is there a Turing machine $T$ taking two inputs such that $\forall m \forall n \exists q \; T(m; n) = q \land U(q;0)=U(m;n)$? It seems "obvious" that ...
raoof's user avatar
  • 75
14 votes
5 answers
5k views

Is it provably true/false that for a program, there exists a proof whether it halts or not?

A standalone statement of my question Given a program that takes no argument, we are interested in whether the program will eventually terminate. My question is this: Theoretically speaking, can we ...
DatoClement's user avatar
2 votes
1 answer
465 views

Disprove: if L is decidable then Prefix(L) is decidable

The following question was sent to me by a friend and I didn't really ask him about its source so I couldn't provide the source of it. I solved the question and I need to ensure my answer not just for ...
Mohamad S.'s user avatar

1
2 3 4 5
9