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
0
votes
1answer
50 views

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 $F$ ...
0
votes
0answers
58 views

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 ...
5
votes
1answer
301 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
votes
1answer
42 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\...
-1
votes
1answer
152 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
votes
2answers
48 views

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
vote
0answers
254 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 ...
1
vote
2answers
86 views

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
votes
1answer
196 views

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 ...
0
votes
3answers
332 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 ...
2
votes
1answer
194 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 ...
-3
votes
1answer
156 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 ...
-1
votes
1answer
62 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
vote
1answer
79 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
votes
1answer
63 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
votes
1answer
75 views

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 ...
0
votes
0answers
31 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
197 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 $M$ ...
3
votes
1answer
118 views

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
203 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
53 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) ?
4
votes
0answers
101 views

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 ...
-2
votes
1answer
72 views

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
351 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
vote
1answer
200 views

Counter Machine (Halting Problem)

How can we show that Halting Problem for one-counter additive machines is decidable ?
-1
votes
1answer
104 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
votes
1answer
97 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
155 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
116 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
votes
1answer
90 views

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 ...
1
vote
0answers
33 views

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
339 views

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 ...
1
vote
1answer
289 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
votes
1answer
59 views

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
133 views

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)?
0
votes
1answer
117 views

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
votes
1answer
120 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
votes
2answers
136 views

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
votes
2answers
394 views

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 ...
3
votes
2answers
90 views

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 ...
1
vote
1answer
755 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
vote
0answers
27 views

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 ...
1
vote
1answer
25 views

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....
-4
votes
1answer
348 views

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
votes
3answers
627 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
votes
1answer
77 views

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
846 views

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
votes
0answers
61 views

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 ...
2
votes
1answer
93 views

What is the current state of the art in solving the halting problem? [closed]

Yes, I know it's uncomputable in the general case. What I want to know is what special cases have been solved, and if there is work ongoing on finding or developing more of them. To be a little more ...
1
vote
1answer
137 views

Turing decider Halting Problem

Wiki and my classes Textbook defines a decider as: In computability theory, a machine that always halts—also called a decider (Sipser, 1996) or a total Turing machine (Kozen, 1997)—is a Turing ...

1
2
3 4 5
7