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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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 ...
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1answer
44 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 ...
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26 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?
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43 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 $M$ ...
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1answer
63 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 ...
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1answer
45 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
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1answer
26 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) ?
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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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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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2answers
69 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 ...
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1answer
118 views
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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60 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 ...
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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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2answers
89 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 (...
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1answer
74 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 ...
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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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2answers
102 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 ...
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1answer
109 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:
"...
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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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2answers
110 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)?
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1answer
59 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 ...
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1answer
42 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 ...
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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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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 ...
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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
163 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 ...
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0answers
23 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 ...
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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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311 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 ...
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2answers
198 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.
$$L_{1} = \overline{HALT_{TM}} = \big\{ \langle M, ...
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if an argument of a lambda only passes itself if it is further evaluated, is runtime always finite?
In order for a lambda expression to run forever, there must be at least one lambda in the expression
in which an argument is passed to itself. For example the following runs forever.
$$
(\lambda x.xx)...
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2answers
709 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 ...
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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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1answer
80 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 ...
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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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2answers
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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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1answer
448 views
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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1answer
56 views
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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1answer
62 views
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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0answers
25 views
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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1answer
290 views
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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1answer
432 views
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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5answers
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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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2answers
45 views
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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5answers
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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.....
