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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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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 ...
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Everytime I convert a PDF to PNG it becomes more pixely, how can I fix it? [closed]

The pdf file I use is high quality, and if you were to zoom at a letter as much as Adobe Reader can handle, you still find it difficult to look at a blocky pixel at the edges of a letter. But when I ...
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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) ?
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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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Classify Turing Machine as Decidable, Co-recognizable, Recognizable

$L = \{ \langle M \rangle \mid $ $M$ is a TM and $M$ visits its start state at least twice when executed on ε$\}$. Prove whether $L$ is decidable, recognizable or co-recognizable. I think the ...
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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)...
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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 ...
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Counter Machine (Halting Problem)

How can we show that Halting Problem for one-counter additive machines is decidable ?
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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 ...
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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 ...
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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 ...
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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 (...
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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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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 ...
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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
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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: "...
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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 ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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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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 ...
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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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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 ...
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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, ...
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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)...
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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 ...
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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 ...
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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 ...
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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 ...
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Does the undecidability of the halting problem require Turing Machines to be enumerable?

I (think I) understand the enumeration and then diagonalization proof of the undecidability of the halting problem, but I came cross this proof in SICP below, which does not seem to require the ...
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Prove that $H$ reduces to $H\varepsilon$

I have to prove that $H_\varepsilon = \{<M> \mid M\ \text{halts on input }\varepsilon\}$ reduces to $H$ (the halting problem). I am very confused how to PROVE it, I mean it is clear that we can ...
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Can a weaker version of the Halting Problem be solved?

I've been learning about the Halting Problem and the proof that it is undecidable in its general case. The proof that it cannot be solved generally goes something like this: Assume that some machine $...
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Is the halting problem theorem really proven

Here is a popular proof of the halting problem theorem: Suppose there exist a procedure h(x, y) so that for any procedure p(x) and any data d, the execution of h(p, d) will halt, where halt means ...
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How to proof HALT doesn't reduce to L?

What method(s) can I use in general to proof HALT doesn't reduce to given language?
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The halting problem for laymen [duplicate]

This line from Wikipedia made me want to ask this question: There is, however, no general procedure for determining whether an expression involving looping instructions will halt, even when humans ...
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How strong “Consistent Guessing Problem” is?

I saw "Rosser’s Theorem via Turing machines" at: https://www.scottaaronson.com/blog/?p=710 The modified halting problem (Consistent Guessing Problem) CGP is used in the proof: ...
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Prove that a language is undecidable by reducing HALT to it [duplicate]

Let $L = \left\{ \langle \alpha, x\rangle \mathrel{}\middle|\mathrel{} \textrm{x is the only string accepted by}\mathrel{}M_\alpha \right\}$ and $HALT = \left\{ \langle \alpha, x\rangle \mathrel{}...
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Are the implications of the diagonalization language different from those of the halting problem? [duplicate]

Revised: In my previous question, I was confused about the implications of the diagonalization language. I concluded that it proves there are languages for which there are no recognizable turing ...
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How does reducing the Halting problem prove the reduction cannot exist?

For example, take the problem "Does M Halt on the Blank Tape?". My approach was to reduce the halting problem to prove this problem is also undecidable. I generated a Mw by Writing w on the tape ...
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How to prove the existence of a number which cannot be written by any algorithm?

I have the problem: Show that there exists a real number for which no program exists that runs infinitely long and writes that number's decimal digits. I suppose it can be solved by reducing ...
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What does the halting problem mean for a Babbage machine?

I read that the Babbage machine is Turing complete. Which means that no decision Turing machine will halt on the question "does the Babbage machine computes the logarithms of its input?" (for example)....
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Turing machine + time dilation = solve the halting problem?

There are relativistic spacetimes (e.g. M-H spacetimes; see Hogarth 1994) where a worldline of infinite duration can be contained in the past of a finite observer. This means that a normal observer ...
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how to prove that the diagonal language K is r.e

To prove that K= $\{x \mid \phi_x(x)$ halts and accepts$\}$ is r.e.: we can recognize K by: for any x, we simply run x on machine $\phi_x$ and accept if the machine accpets else reject and that's it.....
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How to properly reduce a set of TMs to the halting problem?

Consider a standard enumeration of Turing machines ($T_0, T_1, T_2$, ...). Then, let language A be defined as $A = \{n \in\mathbb N | T_n(\lambda) \downarrow\}$. I need to reduce it to the halting ...
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how to mapping reduce any r.e. language to the diagonal language K?

We know that the halting problem $A_{TM}$ and the diagonal language K are mapping reducible to each other. Furthermore both are complete with respect to the mapping reduce relation. I would like to ...
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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 ...