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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questions
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Halting problem proof is wrong, here is why
Instead of solving the halting problem, I will try to solve a less complicated problem in a similar manner.
Can we write a function that will predict if two given numerical inputs are equal.
I will ...
2
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1answer
33 views
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 ...
5
votes
1answer
264 views
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 ...
0
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1answer
30 views
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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1answer
60 views
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?
0
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1answer
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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:
...
1
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0answers
103 views
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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0answers
51 views
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, ...
0
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0answers
10 views
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 ...
1
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2answers
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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 ...
2
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1answer
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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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2answers
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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 ...
2
votes
1answer
46 views
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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1answer
60 views
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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1answer
60 views
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 ...
1
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1answer
39 views
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 ...
0
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1answer
53 views
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 ...
2
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1answer
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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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0answers
27 views
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?
4
votes
2answers
70 views
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 $M$ ...
1
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1answer
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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 ...
2
votes
1answer
54 views
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 ...
2
votes
1answer
30 views
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) ?
2
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0answers
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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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1answer
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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)...
3
votes
2answers
100 views
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 ...
1
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1answer
139 views
Counter Machine (Halting Problem)
How can we show that Halting Problem for one-counter additive machines is decidable ?
1
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1answer
55 views
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 ...
0
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1answer
68 views
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 ...
2
votes
2answers
103 views
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 ...
0
votes
2answers
96 views
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 (...
0
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1answer
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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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0answers
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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 ...
1
vote
2answers
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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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1answer
134 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:
"...
0
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1answer
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Halting problem with extra input
Can there be a function HALT(f, y) so that:
There are some x such that f(x) halts iff there ...
3
votes
2answers
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Is it possible to write a program that calculates an algorithm's time complexity? [duplicate]
Title is self explanatory.
I have searched here on this site and haven't found any discussion about this.
Is it somehow related to Turing's Halting problem (which is undecidable)?
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1answer
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Is this language recognizable?
Let $L = \{M: M\text{ halts on only one of 1100 or 0011 or 0011 or 1000}\}$. I'm trying to determine whether $L$ is decidable.
I don't think it's even recognizable, but I'm not sure. Regardless, I ...
0
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1answer
66 views
Define the following problem as a language and prove that it is undecidable with a reduction from the halting problem.
...Knowing whether a Turing machine will ever output your name on the tape. The language is the set of all TMs that print your name. Reduce from HALT TM.
I had this problem on my exam. From my ...
4
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2answers
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Converse of halting problem
It is well known that if some computing apparatus is Turing-complete, then the halting problem is undecidable for that computing apparatus. However, is it true that if the halting problem is ...
3
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2answers
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Does Halts reduce to all other undecidable languages?
In a CS theory class I'm taking, we showed Halts was undecidable via a diagonalization argument. All other undecidable problems we looked at we either got by reducing Halts to them, or some chain of ...
2
votes
2answers
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Why did Alan Turing have to define computation before demonstrating undecidability?
It seems to me that Turing could've just presented the following argument:
Theorem: Given a computational model $\mathcal{M}$ capable of conditional branching and indeterminate repetition the halting ...
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1answer
230 views
Prove if a property of a Turing Machine is decidable or not, how can I do it?
I cannot understand how to prove if a certain property of a Turing Machine M is decidable or not.
For example, if a have this:
(1.1) "M always halts within 100 steps"
or this
(1.2) "M recognizes ...
1
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0answers
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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 ...
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1answer
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does there exist for each program that produces a sequence, a program that returns true or false if a number is in the sequence?
let S be the set of all programs that take a natural number as input and return another natural as output. let M be the set of all programs that take a natural number as input and return true or false....
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Is Alan Turing's proof of the incomputability of halting problem invalid?
I fail to see a contradiction in the halting machine proposed by Alan Turing.
Definition of halting machine
Where
H = all possible programs that terminates
N = all possible programs that do not ...
0
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2answers
217 views
Prove or disprove if $L_{1}$ is undecidable and $L_{2}$ is finite language then $L_{1} \cup L_{2}$ is undecidable
I tried to prove by contradiction.
$L_{1}$ is undecidable and $L_{2}$ is finite language then $\overline{L_{1}}\cap \overline{L_{2}}$ is decidable.
$$L_{1} = \overline{HALT_{TM}} = \big\{ \langle M, ...
4
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1answer
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if an argument of a lambda only passes itself if it is further evaluated, is runtime always finite?
In order for a lambda expression to run forever, there must be at least one lambda in the expression
in which an argument is passed to itself. For example the following runs forever.
$$
(\lambda x.xx)...
8
votes
2answers
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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 ...
0
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Reduction of HP to L3
I want to make the following reduction:
HP is the Halting Problem: HP = {w#x | w, x ∈ {0,1}* , Mw halts on input x}
w is the binary coded turing machine Mw.
L3 is the problem which asks, if M ...
