Questions tagged [turing-machines]
Questions about Turing machines, a theoretical model of mechanical computation capable of simulating any computer program.
1,513 questions
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Basic Mapping Reduction HALT Question
Here is a language
$L = \{ \langle M \rangle \mid M$ is a TM and $M$ halts on some string that ends with $101$}
I wish to prove this is not co-recognizable by the halting problem $HALT \leq _{m} L$.
...
2
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1answer
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Can such a Turing-recognizable language exist?
Suppose $\Sigma = \{a,b\}$. Is the following claim correct?
There exists a Turing-recognizable language $L \subseteq \Sigma^*$ such as its complement is not Turing-recognizable, and for all $n \in \...
2
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1answer
18 views
Uncomputably coded model of computation
There are many different but equivalent models of computation. I assume their equivalence is shown by coding input of one model to the input of the other model and making an argument why should there ...
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1answer
27 views
Superset of another language and recognizability of turing machines
$L_1$ = $\{\langle M \rangle \mid M$ is a turing machine and $M$ halts on some string$\}$
$L_2$ = $\{\langle M \rangle \mid M$ is a turing machine and $M$ halts on all strings $\}$
a) Is $L_2$ a ...
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1answer
30 views
Is $ L = \{ a^n\ |\ a^n \not\in L_n \} $ Turing recognizable (recursively enumerable)?
Say $ \Sigma = \{a\} $, $M_1, M_2, ... $ is an enumeration of all TMs that recognize languages over $\Sigma$ and $L_1, L_2, ... $ are respectively the languages that are recognized by those TMs. We ...
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1answer
56 views
Are all compilers Turing Machines?
So the definition of a compiler I got is that:
A compiler takes a string as input and checks if that string is syntactically correct, then outputs "Yes" or "No".
So does that mean all compilers ...
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How to adapt proof of the ND time hierarchy theorem for alternate definition of NDTM?
For reference, the version of the nondeterministic time hierarchy theorem in question is this one:
The relevant portion of the proof in question (also from Arora-Barak) is here:
Arora-Barak define a ...
2
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1answer
26 views
One-taped RAM vs Multi-taped RAM
In Turing Machine, we know that there's (fine-grained complexity) difference between one-tape, 2-taped and multi-taped TM, even though they could be simulated efficiently.
(Well, actually I'm not ...
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75 views
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How does a Turing machine with one tape read its input?
It's often implicitly assumed that we don't have to pay much attention to the difference between the program (which specifies the function being computed) and the input (the value on which that ...
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1answer
25 views
Turing machine loop and reject example
I'm getting confused on these both. Reject the string does a stop while loop the machine goes on and on.
My textbook has one example on a reject state and no physical one for loop:
Assume that no ...
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0answers
20 views
Multi-tape to single tape Turing Maching transition complexity
Suppose we have a k-tape Turing machine M and we wanna model it with a Single tape Turing machine N with a register.
Suppose the time complexity of M is T(n):
...
2
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1answer
23 views
Complexity of a Turing Machine when changing its alphabet to binary
I found in 'Computational Complexity: A Modern approach' Book the following statement that i dont quite understand its proof:
For every f : {0, 1}∗ → {0, 1} and time-constructible T : N → N, if f ...
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1answer
26 views
Recognizably turing machine question (reject / loop)
The definition of proving recognizability using dove tailing is below. However I'm wondering if we can also prove loop or reject in the same way?
Give a deterministic TM D that recognizes L such that ...
2
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1answer
28 views
Non-Deterministic Turing machine vs Probabilistic Turing Machine vs Deterministic Turing Machine
What is the difference between a Non-Deterministic Turing machine, Probabilistic Turing Machine and a Deterministic Turing Machine ?
3
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1answer
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Why do we simulate the universal TM to simulate another TM M instead of simulating M directly?
In the proof of the time hierarchy theorem given on page 69 of Arora-Barak, we define a TM D as follows:
"On input $x$, run for $|x|^{1.4}$ steps the Universal TM $\ \mathcal{U}$ of Theorem 1.9 to ...
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1answer
42 views
Advantages of Lambda calculus over Turing machine and vice versa [closed]
What kind of advantages does Lambda calculus have over Turing machine, and vice versa?
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16 views
What's the difference between Acfg and ALLcfg
In computational theory, and talking about CFGs, Turing Machines, and so forth I haven't a satisfactory explanation or definition for what ATM means versus ALLTM or the same or similar uses with ...
2
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1answer
77 views
Can these two languages be reduced to one another?
Given:
$L_1=\left\{ \left\langle M\right\rangle :L\left(M\right)\ni w_{0}\right\}$
$L_2=\left\{ \left\langle M\right\rangle :L\left(M\right)=\left\{ w_{0}\right\} \right\}$
I believe I've managed ...
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1answer
19 views
Prove/Disprove: Every two non-trivial NP-complete problems are decreasing reducible?
We say that two languages $L_1,L_2$ are decreasing reducible if there exists a polynomial time reduction $f:\Sigma^*\to\Sigma^* $ and there exists $n\in\mathbb{N}$ such that for every $x\in\Sigma^*$ ...
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1answer
32 views
Dove tailing questions about accepting language
$L = \{M | \text { M is a TM and there exist some string w that contains five 1's such that M halts}\}$
Where $\Sigma =\{0,1\}$
let $w_1, w_2, \cdots, \in \Sigma^*$ be an effective enumeration. We ...
2
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2answers
87 views
Changing a complete undecidable turing machine language
$L = \{\langle M\rangle\mid \text{M is a TM and }L(M) = \{101\}\}$ meaning M accepts only the string $101$. Which is neither co-recognizable / recognizable. Can be proven easily by $HALT \leq_m L (\...
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2answers
42 views
Are Context Sensitive Languages Turing Complete?
Related questions:
Can regular languages be Turing complete?
Why are Linearly Bounded Turing Machines more powerful than Finite State Automata?
https://stackoverflow.com/questions/14589346/is-c-...
2
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1answer
79 views
How to come up with a language that is recognizable but not co-recognizable?
Forming a language that is recognizable but not co-recognizable. I'm having trouble coming up with a language with these properties. A recognizable language is a language $A \subseteq \Sigma^*$ iff $A ...
2
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1answer
41 views
How to reduce EQU to UNI?
Let $$\texttt{EQU}=\{u\#v \mid T(M_u)=T(M_v)\} \\
\texttt{UNI}=\{w \mid T(M_w)= \Sigma^*\}$$
How can you prove $\texttt{EQU} \leq \texttt{UNI}$?
The idea I have so far is, to simulate the TM that ...
3
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1answer
43 views
How to reduce $\{w \mid |T(M_w)| \geq 42\}$ to the halting problem?
For a string $w$, $M_w$ denotes the Turing machine whose encoding is $w$.
I want to reduce the language $L=\{w \mid |T(M_w)| \geq 42\}$ to $H_0 = \{w \mid M_w \text{ halts on } \epsilon\}$, but I ...
2
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2answers
48 views
Turing machine reduction task
I am having trouble solving the following task:
Given is the language $$D=\{ \langle M, w \rangle \mid \text{$M$ is a Turing machine and $M$ enters all states on input $w$}\}$$
Prove that $D$ ...
3
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1answer
39 views
Pebble game lower bound?
This paper says pebble games have super linear lower bound for every fixed $k$ https://dl.acm.org/citation.cfm?doid=62.322433.
Why is it not considered proof of constructive example for a function in ...
3
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1answer
74 views
How does Rogozhin's (2, 18) universal turing machine work?
I am trying to understand Rogozhin's (2, 18) universal turing machine by stepping
through a simple 2-tag encoding that I believe should loop forever:
a -> aa
...
2
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1answer
28 views
Turing machine diagram for twice number of 0 than 1 [closed]
Can anyone help me with a Turing machine diagram for twice number of 0 than 1
3
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1answer
53 views
Is the language of all TMs *not* accepting a given string, Enumerable?
Is the following language in RE?
$$L = \{\langle M\rangle : M\text{ is a TM that does not accept }010\}$$
I could use Rice's Theorem with the property $P = \{L : 010\text{ is not in }L\}$ to show ...
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1answer
21 views
Universal Turing machine and virtualization technology
I was wondering if virtualization technologies (VmWare, virtual box) are possible thanks to the theoretical existence, translated into practice, of the concept of universal turing machine or if the ...
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0answers
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building turing machine for busy beaverproblem
I have tried to build a turing machine for busy beaver problem that has BB(2,3) two variables and three variables but i am not sure if its correct or it needs any changes
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1answer
19 views
Turing recognizable language between languages that aren't recognizable?
Let $L_{1},L_{2}$ be languages that are not Turing recognizable, and let $L$ be a language such that $L_{1} \subseteq L \subseteq L_{2}$.
Is $L$ also not Turing recognizable?
I am inclined to ...
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1answer
32 views
Efficiently deciding whether TM accepts all inputs in at most $k$ steps
I want to decide if a deterministic TM $A=(Q, \varGamma, \delta, q_s, q_h)$ halts on every input in at most $k$ steps. If the TM $A$ stops after $k$ steps, then the positions $A$ can reach are ...
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1answer
50 views
Is $L = \{ \langle \langle \ M\ \rangle \rangle \ | \ M \ \text{does not accept}\ 010 \} $ Turing recognizeable?
I'm working on the following problem:
Is the following language Turing recognizable (recursively enumerable)
?
$$L = \{ \langle \langle \ M\ \rangle \rangle \ | \ M \ \text{does not
> ...
2
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1answer
29 views
How To Show That B is Semi-Decidable Given A
I am preparing for my Computational Theory final and ran into this exact problem :
B={ x | there exists a prefix of x that is in A}.
Show that B is semi-decidable. In other words, you need to ...
1
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1answer
69 views
I have trouble translating Turing machine language, can you help me break down language notation to English?
My problem is I don't have many issues with creating a Turing machine state table when given a string such as 01101, my issue arises when I am presented with a problem which requires the Turing ...
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2answers
56 views
How is diagonalization a valid argument for the undecidability of the halting problem?
All proofs for the undecidability of the halting problem seem to be based directly or indirectly on self-reference.
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2answers
59 views
Is finding a single digit of a computation is as hard as finding the computation?
Let $f: \mathbb{N} \rightarrow \mathbb{N}$ a computable function such that computing $f(n)$ takes $\Omega(2^{2^{2^{|n|}}})$ time in worst case terms and such that the languages:
$$\begin{align*} L_1 &...
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1answer
56 views
how can this function be computed in polynomial time in regards to its input?
i am struggling for quite a while with this. trying to understand why the following function can be calculated in polynomial time(in regards to the input length)
defining a function from assignments ...
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3answers
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Why is the blank symbol not considered part of the input alphabet of a Turing machine?
Definitions of Turing machines are always explicit about the blank symbol not being part of the input alphabet.
I wonder what goes wrong when you would make it part of the input alphabet, because ...
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1answer
36 views
How precise to be when describing a Turing machine?
I'm kind of new to the theory of computation and I was working on this problem:
We say that a Turing machine $M$ uses $k$ squares of tape for an input string $w$ if and only if there exists a ...
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1answer
37 views
Randomized Algorithm in $O(d)$ for Solving Unknown Degree $d$ Polynomial Function Using an Erroneous Oracle
Consider the field $GF(p)$, where $p$ is a prime number. If there is a function $f: GF_p \times GF_p \rightarrow GF_p$ which has an unknown degree $d$ polynomial, with $1 < d < p / 4$.
Although ...
4
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1answer
62 views
Prove the probability of which a hash function is collision-free
Suppose $H = \{h_1, ..., h_T\}$ be a family of pairwise independent hash functions mapping $\{0, 1\}^n$ to $\{0, 1\}^{n/2}$. Let $M = \frac{2^{n/4}}{10}$ and let $x_1, ..., x_M$ be any M distinct ...
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0answers
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Theory for programs that are “embedded” in other programs?
We can make the following distinctions: (I will use the term "program" and "machine" as synonyms).
A (baseline) machine. This can be formalized by a Turing machine. It receives an input, and computes ...
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1answer
74 views
What's the purpose of the non-deterministic Turing machine?
(*) Acronyms
NTDM := non-deterministic Turing machine.
TM := deterministic Turing machine.
(*) Consider the following idea
The NTDM is able to follow, in parallel, all paths of the tree of the ...
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1answer
26 views
What is the relation between an algorithm and its implementation at the level of code?
Is there any isomorphism or equivalence relation? What strictly bind these two together?
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2answers
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Does this article imply that Turing-Computability is not the same as “effectively computable”?
First of all, I apologize if this has been asked, but I truly didn't find anything.
I've stumbled across this article. It says that there is a problem that only Quantum Computers can solve.
In my ...
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2answers
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Describe in words how a NTM can simulate a DTM
I have this assignment
Describe in words how a DTM can simulate a NTM
Describe in wordshow a NTM can simulate a DTM
I'm working on this request and I'm crushing with the comparison.
1-I ...
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2answers
46 views
Draw a Turing machine that decides the language of all words over the alphabet {a, b} that have an odd number of a’s and an odd number of b’s
Does the question mean draw a Turing machine that takes input with any number of a's and any number of b's (eg. aaabbb, ab, abababab, etc.). The turing machine should only then accept or reject the ...
