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Questions tagged [turing-machines]

This tag is suited for questions involving Turing machines. Not to be confused with finite state machines and finite automata.

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Does/Can a “function” exist that can “return” “any” “number series”?

I am really a novice at Math and am interested in the existence of such function as I think it could be really useful for some experimentation in machine learning. My question is, does/can a "...
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Having trouble determining what Turing machine evaluates?

While learning about Turing machines, I've stumbled onto a problem that I'm not sure how to solve. I've put a lot of work into trying to find the solution, any help would be appreciated. The problem ...
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1answer
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Five shortest strings from language $ L = \{0^{i}1^{i}| i \in \mathbb{N} , i > 0\}$

I am studying for an upcoming exam, with an example question being. Consider the following language, $L = \{0^{i}1^{i}| i \in \mathbb{N} , i > 0\}$ Over the alphabet $A = \{0,1\}$ What are the ...
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Is Langton's Ant really Turing Complete

I recently watched a Numberphile video about Langton's Ant (and the extra footage). They mention that the ant always ends up creating a highway at some point in all the initial board configurations ...
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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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Turing Machine for vertex cover

Give a polynomial-time Turing Machine which, given a graph G and an integer k as input, will halt and output a vertex cover of G of size at most k — that is, it halts with the encoding of an actual ...
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Classify Turing Machine as Decidable, Co-recognizable, Recognizable

Consider the language L = {: M is a TM and M visits its start state at least twice when executed on ε}. Prove L with respect to decidability, recognizability, and co-recognizability. I think the ...
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How can I estimate Turing machine running time?

I try to evaluate working time of Turing machine. I understand, I have to calculate number of steps used in every stage. My problem is: how can I know, how many steps used in every stage, for example, ...
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How can I prove the following question?

For every time constructible function T, if L is in TIME(T(n))(or more specifically D-TIME) class, then there exists an oblivious Turing Machine M that decides L in O(T(n) log T(n)) time.
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Deterministic Turing machine for the language L = {x ∈ {0, 1} ∗ | x is not of the form 0w1w for w ∈ {0, 1} ∗}.

All right so, for this I don't need to graphically show the Turing machine, but rather just describe the process. I feel like I can do this on my own, but I'm having a little trouble starting. I'm ...
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Prove that the following language is decidable / undecidable

Part A) Prove that the following language is decidable: Input: The description of a DFA A. Output: YES if A accepts the empty string. NO if A does not accept the empty string. I am struggling ...
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Why do results shown by diagonalization relativize?

my textbook mentions: "Using an oracle $O$ to show $L \neq B$ then for every oracle $X$ $L^X \neq B^X$. So this fact isnt very intuitive to me. Can someone please help ?
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Hopping to infinity along a string of digits

Let $s$ be an infinite string of decimal digits, for example: \begin{array}{cccccccccc} s = 3 & 1 & 4 & 1 & 5 & 9 & 2 & 6 & 5 & 3 & \cdots \end{array} Consider ...
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2answers
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Ordering of Turing machines?

I am new to Turing Machines. As in I’ve been reading about them over the last two days. So I am not very knowledgeable at this moment. I was also reading about the Kleene’s O system of ordinal ...
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1answer
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$Show\:that\:B_A=\left\{w\in \sum ^{\ast }:\:\exists \:x\in \:A\:s.t\:\left|x\right|\le \left|w\right|\right\}\:is\:decidable\:$

$A\:is\:some\:language\:over\:\sum.\\Show\:that\:B_A=\left\{w\in \sum ^{\ast }:\:\exists x\in A\:s.t\:\left|x\right|\le \left|w\right|\right\}\:is\:decidable\:$ I thought to show a non-deterministic ...
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what is the mapping reduction of $A_{TM}$ to $\overline{CF_{TM}}$

first post here :) I am trying to find a reduction from $A_{TM}$ to $\overline{CF_{TM}}$. definitions: $CF_{TM}\:=\:\left\{<M>| M\:is\:a\:TM\:and\:L\left(M\right)\:is\:a\:context-free\:...
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Proving Turning Decidable's

Prove that L CFG \ L RG is Turing-decidable, where L CFG = {< G, w > G is a CFG that generates string w}. L RG = {< G, w > G is a regular grammar that generates string w} In relation ...
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1answer
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Enumerator printing out strings from a language

Write down the algorithm of an enumerator that prints out EXACTLY ONCE every string in the language L = {7m+ 2 | m ∈ N} over the alphabet A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. In regards, to the ...
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How to show that if $L(M) \in NP$?

An M deterministic Turing Machine finishes with an n long input in $ \left( n^{100} + 2^{\log{n}} \right)n^2 $ steps. Show that if $L(M) \in NP$. I'm having problem with this exercise. Could someone ...
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let $L = \{\langle M \rangle \mid M \text { is a TM, } \forall x \in L(M), x^R \notin L(M)\}$. Prove/disprove $L\in RE \backslash R$

let $L = \{\langle M \rangle \mid M \text { is a TM, } \forall x \in L(M), x^R \notin L(M)\}$ ($x^R$ is the reverse of $x$) I need to determine and prove whether $L\in R , L\in RE \backslash R, \...
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is there a linear bounded automaton the decides $A_{nfa}$?

first post here :) I was wondering, since regular languages are context sensitive, and since linear bounded automatons can act as an acceptors for context sensitive language, is it possible or is ...
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1answer
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Diagonal argument applied to computable numbers

Upon applying the Cantor diagonal argument to the enumerated list of all computable numbers, we produce a number not in it, but seems to be computable too, and that seems paradoxical. For clarity, ...
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1answer
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What does it mean for a number to be independent of ZFC?

Since the definition of the Busy Beaver function by Radó in 1962, an interesting open question has been what [is] the smallest value of $n$ for which $BB(n)$ is independent of ZFC set theory. Source: ...
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Prove the languages |L<M>| = 2 and |L<M>| $\not=$ 2 to be non-Turing recognizable or non-recursively enumerable

I am trying to prove the non-recursively enumerable property of two languages. L = {$\langle M \rangle$: |L$\langle M \rangle$| = 2}. and L = {$\langle M \rangle$, |L$\langle M \rangle$| $\not=$ 2}. ...
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How to prove {e: L($M_e$} is decidable} is not Turing-recognizable?

I have reduced {e:$M_e$ accepts e} to this one. But I failed to reduce in the other direction. And I don't know if there is an algorithm to solve this. Thank @Noah Schweber who tells me it's not ...
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L = {$(n,w)$ $w$ is a binary representation of the n-th fibbonacci number} membership decision problem

I am a student currently studying Computational Models. I still don't have a full understanding of the subject and was wondering about languages of the form $L = \left \{(n,w) | f(n) = w \right \}$ ...
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1answer
133 views

Difference of two decidable languages?

I've been learning about TMs in class lately and we talked about the decidability of two languages by union or intersection. I was wondering if you have two decidable languages, L1 and L2, is their ...
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Complexity of a copy and reverse Turing Machine

I have a turing machine, that appends a reversed copy of a string to the end of the string. The alphabet of the TM is {a, b}. Copy & Reverse TM How can I prove the time complexity of this Turing ...
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Turing Machines recognizing the same language

Is it possible for two turing machines that take different types of inputs, for example $\langle M,w\rangle$ and $\langle M\rangle$, to recognize the same language?
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What rule allows to determine the symbol on an $i$-th cell of the tape of an Infinite Time Turing Machine at any limit stage?

Assuming that $s$ denotes a particular symbol that can appear on the tape, $\alpha$ denotes any limit ordinal such that $\alpha \ge \omega$ and $C_i[\tau]$ denotes the symbol on the $i$-th cell of ...
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1answer
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Can we enumerate finite sequences which have no halting continuation?

Note: this is a cross-post from CS.SE, since I haven't gotten an answer there. I am trying to deepen my understanding of the relationship between the Halting Problem and Godel's Completeness Theorem (...
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1answer
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$\delta:Q\times\Gamma\to Q\times\Gamma\times\{L,R\}$: how to convert this statement in $f(x)$ form?

$\boldsymbol{\delta:Q\times\Gamma\to Q\times\Gamma\times\{L,R\}}$: this equation represents the transition function of deterministic Turing machine. How can i convert it in $f(x)$ form, like $f:x\...
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1answer
81 views

How to prove or disprove that a machine is Turing Complete?

Given a set of operations machine can perform, how to prove or disprove it's Turing Completeness? Is the definition of a set of operations and corresponding state changes is enough or should I add ...
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Specify a decisive Turing machine that calculates the following function $f$.

Specify a decisive Turing machine that calculates the following function $f$: $$\small f:\{a,b\}^*\to\{a,b\}^*\textrm{ with } f(w)= \begin{cases} (bba)^{3\cdot\#_b(w)}& \text{if } \#_a(w) \text{ ...
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1answer
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Where is the theorem related to the construction of countable admissible ordinals by Turing machines with oracles?

Wikipedia contains the following information in the article "Admissible ordinal": By a theorem of Sacks, the countable admissible ordinals are exactly those constructed in a manner similar to the ...
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Correctness proof: induction on sequence of steps, need a stronger claim?

Im trying to prove the correctness of the construction proposed in this CS-SE answer: a two stack PDA that simulates a Turing Machine. By "correctness" i mean to prove more or less formally that we ...
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Is classical Euclidean geometry Turing complete?

By "classical Euclidean geometry" I don't mean the study of $\mathbb R^2$ with the Euclidean metric, or a model of Hilbert's Grundlagen axioms, or the study of those properties of $\mathbb R^2$ that ...
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does the language 𝐿 = {< 𝑀1 >, < 𝑀2 >: 𝐿(𝑀1 ) ⊆ 𝐿(𝑀2)} is in co-RE?

i was asked to determine if its in RE and if its in co-RE. well i think its easy to say the language is not in RE but i was wondering if this language is in co-RE. so the question is if $\overline{L}$...
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Is it possible to put a topology on Turing-recognizable languages to express density among all the languages?

In a Calculability and complexity course I had at univeristy, we proved that there exist languages that are not Turing-recognizable basiclly using Cantor's diagonal argument (the set of all languages ...
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How can I prove that binary multiplication decision problem is solved in O(logn) space?

I can prove this if I use a NTM Turing Machine, but it is required to use a two-taped DTM, while taking into account only the space of the second "work tape"
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Is there a name for this type of turing machine?

I'm considering the turing machines with the following form: $(Q,\Gamma,b,\Sigma,\delta,q_0,F)$ where the tape symbols,$\Gamma$ are $\{0,1\}$, so the input symbols, $\Sigma$ must be $\{1\}$ and the ...
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1answer
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Decision function uncountable, why?

Good morning guys, I'm a new user of StackExchange, and I have already found here: Set of decision functions are uncountable However, I do not really understand the answer. I'm a student of Computer ...
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1answer
44 views

Finding languages such that $L_1\subset L_2\subset L_3$ where $L_1,L_3\notin$ RE and $L_2\in$ R [duplicate]

I am struggling to find such languages $L_1$, $L_2$, and $L_3$ such that $L_1\subset L_2\subset L_3$ where $L_1,L_3\notin$ RE and $L_2\in$ R. I know they exist, I need help finding them.
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1answer
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Minimum Number of states turing machine

I think my question is rather simple, but I can't wrap my head around it. In "The (new) Turing Omnibus" on page 266, the author writes: [...], and let A be a [Turing-]machine that converts a blank ...
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Finding languages such that $L_{1} \subseteq L_{2} \subseteq L_{3}$ where $L_{1}, L_{3} \notin \mathbb{R}$, $L_{2} \in \mathbb{R}$

I am struggling to find such languages $L_{1}$, $L_{2}$, and $L_{3}$ such that $$ L_{1} \subseteq L_{2} \subseteq L_{3} $$ where $L_{1}, L_{3} \notin \mathbb{R}$ and $L_{2} \in \mathbb{R}$. I know ...
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Definition of partial function using predicate that is possibly undecidable

I am reading Kleene's "Mathematical Logic" $2002$ pp 242-246. Let $T(i,a,x)$ stand for: $i$ is the index of a Turing machine (under particular enumeration) which when applied to $a$ as an argument ...
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exhibiting a turing machine and a λ-term of a boolean function

I have a funtion f: BOOL ⇒ Bool, sich that f(x,y) is true when x=y and false otherwise. Im trying to exhibit a touring machine and a lambda term. for the second part I know that in boolean logic, x ⇒ ...
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How to prove that models of indirect and direct RAM machines are equivalent?

as in the title, I am looking for a formal proof how to show that models of indirect and direct RAM (random-access) machines are equivalent. I would really appreciate your help.
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156 views

Turing machine with read only part and finite tape

Given a Turing machine whose input part is read only , and in addition to the input part has a finite tape of length K, prove that this is equivalent to a DFA. I tried to find some bound for the ...
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1answer
138 views

What is the source of formal descriptions for large uncomputable ordinals clockable by Infinite Time Turing Machines?

I can imagine the process of analyzing the computation of an ITTM at any limit stage denoted by $\alpha$ if $\alpha$ is a computable ordinal: basically, we take the description of some standard Turing ...