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

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4
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1answer
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Decidability of halting problem for DPDAs with $\epsilon$-transitions?

For LBAs it's rather easy to prove the decidability of the halting problem, as there can only be a finite number of different configurations when using limited space. But what about PDAs with $\...
0
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1answer
24 views

When reducing from HALT, can you create a Turing machine that asks whether a simulation stops?

Lets say I am doing a reduction from $\mathrm{HALT}_{\mathrm{TM}}$ to another language $S$, in order to prove that $S$ is not decidable. For this I need to build a new Turing machine, $M'$. Can I ...
4
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2answers
56 views

Resource bounded reductions for RE-Complete problems

Given that the halting problem is RE-Complete, we can reduce any problem in RE to an instance of the halting problem. Are there are any results on the time-bounds for this reduction? Can we do this ...
1
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2answers
97 views

Does the the undecidability of the Halting Problem eliminate the possibility of 'Hard AI'? [duplicate]

I'm defining 'Hard AI' as a human-equivalent intelligent machine, or beyond that. Contrast with 'Soft AI' the type of software that runs on your email filter for example. I've been chewing on this ...
2
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2answers
49 views

Does the Halting Problem have practical relevance? I can calculate all outputs for a finite number of states and inputs [duplicate]

Coming from a digital functional hardware verification background, I don’t really understand the Halting Problem. I can represent the program as a state machine and show whether all inputs in all ...
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0answers
19 views

Is a union of any TM language and the halting problem language decidable [duplicate]

I need to find if the following language is decidable (in $R$): $L=\{ \langle M \rangle \mid M \text{ is a TM}, L(M)\cup H_{TM}\in RE\}$ Where $H_{TM}$ is of the halting problem. My intuition is ...
3
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1answer
94 views

Does the Halting Problem prove that true Artificial Intelligence is impossible?

The Halting Problem demonstrates that there are things that a machine can never be programmed to do. Is this proof that true Artificial Intelligence - that is, the ability for a machine to think and ...
1
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0answers
48 views

Is $f$ which returns the $n$-th word in $\overline{H_{TM,\epsilon}}$ computable?

The question itself: Let $f:\mathbb{N}\to\Sigma^\star$ be such that $f(n)$ returns the $n$-th word in $\overline{H_{TM,\epsilon}}$ (which is the complement of the language of TMs which accept $\...
3
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1answer
38 views

Theoretical justification of “halting problem avoidance”

The wikipedia page for the Halting problem mentioned practical solutions to avoiding the halting problem such as avoiding infinite loops. And there is a mention that "by restricting the capabilities ...
1
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1answer
47 views

A question about halt (or stop) of Turing machine

I try to understand something: At Turing machine we have two stats: $q_{accept}$ and $q_{reject}$. Now, if machine $M$ runs on word $w$ (I hope I write it right...) and the final configuration is: $...
0
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1answer
50 views

Axioms - proof of halt

I am new to this forum and this is my first post. I am interested in solving a problem, but cannot find the way to think about it. If anyone can guide me through it, I would be obliged: Let F be some ...
1
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1answer
37 views

Removing $\epsilon$ transitions in a NPDA

NPDA's and general NFA's may not halt for finite inputs like DFA's do because of their $\epsilon$ transitions. However, NFA's with $\epsilon$ transitions could be converted to those without any $\...
7
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2answers
1k views

Is it possible that the halting problem is solvable for all input except the machine's code?

This question occurred to me about the halting problem and I couldn't find a good answer online, wondering if someone can help. Is it possible that the halting problem is decidable for any TM on any ...
7
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3answers
796 views

Undecidability of telling if a program returns true or false

Consider the problem of taking an input Turing machine and determining if the final cell is a $0$ or $1$ after computation halts. On cases where it writes something else or does not halt, you are ...
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2answers
78 views

What does it mean to be Turing reducible?

I'm confused about what it means to be Turing reducible. I thought I understood what it meant, but apparently not. $A \leq B $ Means that A is Turing reducible to B. This means that given an oracle ...
3
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1answer
268 views

Show that the Halting problem is reducible to its complement

HALT$_{TM}$ is the set of all machine-input pairs $<M,w> $ where $M$ halts on input $w$ The complement of HALT$_{TM}$ is the set of all machine-input pairs $<M,w> $ where $M$ ...
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0answers
15 views

IsDefined predicate computable?

I am working on a computability assignment, I want to define a helper predicate IsDefined by: $IsDefinied(x,n) = \{ 1$ if $\Phi^{(1)}(x,n)$ is defined, $0$ otherwise. Where $\Phi^{(1)}$ is the ...
1
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1answer
175 views

Proof by Reduction: From Empty Language to Halting Problem on Empty Input

Question: Let language $E$ = {$\langle M \rangle$ | $M$ accepts no inputs whatsoever} Let language $H$ = { $\langle M \rangle$ | $M$ halts on an empty string input}. Is it possible to show that $H$ ...
0
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2answers
259 views

Understanding proof for Busy Beaver being uncomputable

I found this proof on http://jeremykun.com/2012/02/08/busy-beavers-and-the-quest-for-big-numbers/ and have highlighted the part I don't understand in bold. (BB(n) is defined as the number of steps ...
1
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1answer
78 views

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~...
10
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1answer
284 views

Is the halting problem decidable for 3 symbol one dimensional cellular automata?

I've been trying to figure out if the halting problem is decidable for 3-symbol one-dimensional cellular automata. Definition Let $f(w,i)$ denote the configuration of the system at time step $i$. ...
2
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1answer
56 views

With a halting oracle, can tell whether something will have finite output?

A program can have finite output, yet still not halt. Example: 1: output "Yolo" 2: output "" 3: go to step 2 This only ever outputs "Yolo", despite never halting....
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0answers
35 views

What language features would I need to remove from a real programming language to make it decidable? [closed]

Let's say that I want to restrict certain features of a common programming language--for instance, C--such that the result is decidable, and thus no longer Turing-complete. What language features, at ...
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2answers
112 views

Why does the proof of undecidability of $A_{TM}$ require the universal TM to take input $\langle M,\langle M\rangle\rangle$?

I've read a proof explaining why $A_{\mathrm{TM}}$ is undecidable, and I don't seem to understand why we need to give the opposite of $H$ function $D$ itself as input. Here's the copy-paste of that ...
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2answers
90 views

Can we enumerate provably non-terminating functions?

In trying to understand the Halting Problem better, I am trying to come up with classes of provably non-terminating programs. For example, any program (including input) which leads to a finite-...
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0answers
22 views

Difficulty in the halting problem for a simple Turing machine with standard enumerations of programs and of initial tape configurations

Preparations Consider a Turing machine with just one head and one tape (on which the head may move left, move right, or remain stationary), and with just two symbols ("blank" and "non-blank"). The ...
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0answers
43 views

What can be said about the Halting Problem if we can include the halting status to the input?

I was reading about Turing Machines and the Halting Problem, i understand that you need an oracle to decide whether given input will halt or loop forever. But why do we need an oracle if we can ...
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0answers
108 views

Reducing the halting problem to the uniform halting problem

As stated here https://books.google.cz/books?id=dwpeNRgjK68C&pg=PA57&lpg=PA57&dq=uniform+halting+problem&source=bl&ots=qsbv_672W9&sig=NDcebhxrwcYdF-P15dor565l8Jc&hl=en&...
3
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1answer
52 views

The halting problem of Turing machines in view of enumeration of initial tape configurations

As far as I know, presentations of the (general) halting problem (cmp. Wikipedia) are referring explicitly to an ennumeration of (applicable) programs. For the purpose of my questions let's consider ...
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2answers
368 views

Is how much memory a program needs computable?

We know that how much time a program needs is not computable. Do we know how much memory a program needs is decidable?
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1answer
47 views

Understanding the proof of the halting problem [closed]

I came across the following example that proves that the blank tape halting problem is not decidable. I understand the proof technique, but I just don't see how the blank tape problem is shown to ...
8
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3answers
665 views

Halting problem - one issue that's bothering me

To my knowledge, halting problem asks if there exists a program that decides whether a program being tested, given some input data (no matter what program it is, or what input data we give) will ...
2
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1answer
64 views

Can we use a different encoding scheme to solve an unsolvable language?

Say we have a particular decision problem and that we have an alphabet and an encoding scheme, which gives us a language L that we say is not recursive (i.e. we do not have a Turing Machine that can ...
2
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1answer
254 views

Halting problem without input?

I'm only a layman therefore only discuss stuff naïvely. I read some introductory articles about halting problems with a scenario that if there were such a decider accessible to us, we should be able ...
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0answers
38 views

Is the halting problem a matter of an encoding scheme ?

I was reading about the halting problem recently, there is a video on youtube where it tries to explain the halting problem easily (since it is complicated to explain). So, (A,C & H) have ...
5
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2answers
3k views

Why won't a Turing machine halt?

I am reading Sipsers. The book introduces halting problem and proves that is a turing recognisable language but not a turing decidable language. Thus giving a Turing machine which does not halt on ...
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2answers
74 views

What's the error in the following proof of the halting problem decidability?

Let's encode every state and tape word (with position of Turing machine on it) with a single integer. Then the transition function can be represented as a total function from integers to themselves. ...
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6answers
4k views

What are the simplest examples of programs that we do not know whether they terminate?

The halting problem states there is no algorithm that will determine if a given program halts. As a consequence, there should be programs about which we can not tell whether they terminate or not. ...
0
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1answer
46 views

Showing that the set of DTMs that run forever is not Turing-recognizable

The language A, that is all DTMS that run forever on input. Would this not just be the HALT problem? Therefore no reduction or proof is necessary, other then stating that? ANSWER FOUND: I think i ...
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5answers
3k views

Could the Halting Problem be “resolved” by escaping to a higher-level description of computation?

I've recently heard an interesting analogy which states that Turing's proof of the undecidability of the halting problem is very similar to Russell's barber paradox. So I got to wonder: ...
12
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5answers
532 views

Defining the halting problem for non-deterministic automata

The primary definition of Turing machine (TM), at least in my own reference textbook (Hopcroft+Ullman 1979) is deterministic. Hence my own understanding of the halting problem is primarily for ...
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1answer
84 views

Set of Turing machines that halt after exactly 14 steps [closed]

Let $M_i$ be the Turing machine with Gödel number $i$. Let $$A = \{i \mid M_i \text{ with input \(x\) halts after exactly 14 steps}\}$$ Is the set $A$ recursive?
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7answers
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Is there a more intuitive proof of the halting problem's undecidability than diagonalization?

I understand the proof of the undecidability of the halting problem (given for example in Papadimitriou's textbook), based on diagonalization. While the proof is convincing (I understand each step of ...
0
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1answer
34 views

Decidable Problem

How should I go about showing that the following problem is decidable: Given DFAs M1 and M2, is L(M1) ⊆ L(M2)? What is the general strategy to prove ...
3
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1answer
33 views

Why is it true that the relation R and its negation are not semi decidable?

An example given for a relation R where its negation and itself are not semi-decidable was: $R(x,y)$ holds iff $y = 0$ then $R_{HALT}(x)$ holds, otherwise $y = 1$ and $R_{HALT}(x)$ does not hold. It'...
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2answers
451 views

Turing Machine that computes maximum steps of halting machines

Suppose that $TM_{halting}$ is the set of machines that halt. Given a number of states $m$ and a length $n$ of the input, let $f(m,n)$ be the maximum number of steps a machine with $m$ states in $TM_{...
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1answer
58 views

Trying to understand the proof of the halting problem presented in Sipser textbook

I'm having some problems to understand the classic proof of the halting problem. The Proof: $A_{tm} = ${$<M,w>$ | $M$ is a $TM$ and $M$ accepts $w$}. We assume that $A_{tm}$ is decidable and ...
0
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1answer
591 views

Halting problem reduction to Halting for all inputs

I was going through my book of revision and I would like someone hints on this. The Halt for All Input problem (HAI) takes a machine and tell if this machine halts or not for any input We prove it ...
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1answer
2k views

Halting problem reducing to the blank tape halting problem

I was going through my book of proof and I find very confusing its definition, so I would like someone to help me in understanding this. The blank tape problem takes a machine and an empty tape and ...
3
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2answers
124 views

Halting Problem and Turing Degree and Reduction? [closed]

This is a Local Olympiad question on computation and computer science on 2013. How can explain it and says some hint for understanding such an example question. for $ A \subseteq \mathbb{N}$ we ...