Questions tagged [turing-machines]

Questions about Turing machines, a theoretical model of mechanical computation capable of simulating any computer program.

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A Turing machine with each cell accessed at most $10$ times has an equivalent NFA

I am confused by the following claim: Let $T$ be a (decider, single-tape) Turing machine with the property that for every input, every cell on its tape is accessed at most $10$ times. Then there is a ...
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Are turing machines & equivalents with infinite sized random programs still turing machines?

Are turing machines with an infinite program tape that is completely random, or another example is a Game of Life simulation on an infinite randomly initialized grid, still turing machines, so to ...
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How to simulate an NTM using a DTM?

I've seen questions about how an NTM could simulate a DTM and this seems pretty straightforward to me. However, my text book says you can also simulate an NTM using a DTM. How would this work? I'm ...
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Turing machine with polynomial complexity on Jflap

I would like to ask a question: I have this very simple Turing machine. Simply by subtracting the numbers A and B, given the input M (A, B, C, D) =. Using the Step function on Jflap, complete the ...
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How can a non-deterministic Turing Machine be converted to a deterministic TM with a witness-input?

This 2014 paper by Barak and Goldreich defines the notion of a universal set $S_{\mathcal{U}}$ as the set of all tuples $(M,x,t)$ such that the non-deterministic machine $M$ accepts the input $x$ in $...
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Describe how to build a non-deterministic Turing machine that accepts the set of all element prefixes of $L$, i.e, $PREFIX(L)$

Describe how to build a non-deterministic Turing machine that accepts the set of all element prefixes of $L$, i.e, $PREFIX(L)$. Hello, I have been trying to solve this problem, my intuition tells that ...
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Prove by reduction that the language $L^♦ = \{N | N \text{ is a } TM \text{ and } L(N) \text{ is a recursive language}\}$ is not recursive

Prove by reduction that the language $L^♦ = \{N | N \text{ is a } TM \text{ and } L(N) \text{ is a recursive language}\}$ is not recursive. Hi, I've been strugling with this problem since yesterday, ...
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How Universal Turing Machines can do something if a machine doesn't accept?

In our Computability & Complexity course, we wanted to show that $ALL_{TM}\notin RE$. To do that, we have seen the following claim (I'm summarizing it): Denote the languages: $ALL_{TM}=\{(M)|L(M)=\...
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In the Recursion Theorem, does obtaining a description of SELF increase the length of the program?

In the following video, he mentions that x <- <SELF> (x obtaining a description of itself) is a "legal" operation for a Turing Machine to make. https://youtu.be/5yO_l2w0wIA?t=93 My ...
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Is a computational model that can instantly access any storage address and can access any arbitrary number of them at once more powerful then a TM?

This would be a computational model that would have unbounded space. But with a jump command that can access and do operations on any finite number of cells at once. Actual calculations would take ...
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Turing machine to find maximum of an infinite set

Given a set that is infinite but still countable, does a TM exist that goes over every element in the set and finds the maximum? Is this a computable function?
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Is the following function computable? is it total?

I have the following function: $f : N \to N $ and $f(n)= \max_{i \leq w(n)} g_{i}(n)$ with $g_1, g_2,...g_{w(n)}$ being an enumeration of all computable functions $g_i$, and $w : N \to N$ being any ...
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How to show that the set of all turing machines that halt on a blank tape form a recursively enumerable set

I learned in my class that set of all Turing machines that halt on a blank tape form a recursively enumerable set. I was told that you can prove it using an argument similar to the diagonalization ...
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Simple examples of Recursive Enumerable Functions

My understanding of Recursively Enumerable Functions is that they're recursive functions, but for some values of the arguments you put into the function they will stop and give an answer, and for ...
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Graph based on strings of turing machine

For a $\Sigma$ with characters $0,1,$#$,\sigma_1,...,\sigma_m$. I have any $M$ that is a deterministic turing machine. Fix a $n$ (natural). i look at the following graph constructed from the turing ...
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How do I find out what SPACE a language has?

I want to know how I can calculate/find out which SPACE a language has, because I don't get it. I have this definition Definition: Fix a function $f: \mathbb N → \mathbb N$. We say that a language $A$...
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Proving that a class equals NP ∩ coNP

We say that a non-deterministic Turing machine is nice if for every input x the following holds: • Every computation path returns either ’accept’, ’reject’ or ’quit’. • There is at least one non-quit ...
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Turing machine with infinite tape alphabet

Given is the modified definition of a TM where everything is equal except for one change: $\Gamma=\Sigma\cup \mathbb{N}\cup\{\square\}$ How do I prove that there is a TM $M$ for any language $L\...
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Is it accurate to contrast a Turing machine with finite automata by claiming the former is stateful and the latter is pure?

Recently, I was having a debate with a friend about what it would mean to create a machine that ZKSnarks (proves) itself. I tossed the word pure machine out there while describing what I hypothesized ...
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Can distirbuted processing, OS processes or even threads be used to simulate a non deterministic turing machine adequately on small datasets?

For example for the traveling salesman problem which is a proven NP-Complete problem, if we spawn a thread at each node in the graph such that each of those threads will, in turn, spawn as many ...
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We cannot recognize a set of languages as the language themselves

"We cannot recognize a set of languages as the language themselves" What is the meaning of the line and why we cannot do it and how is the encoding of TM is helping in that?
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Is Self-Modifying Turing Machine equivalent to NTM or TM?

Let SMTM be Turing Machine, but the commands recorded in which can change to others in some random way (for example, choose with a 50/50 probability the command to move to the right or move to the ...
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Small Turing machine accepting single complicated input?

This imprecise question is about a simple example for the following problem. I would like a Turing machine with few states that accepts only inputs which look complicated to the naked eye. Of course ...
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Designing a Turing machine which recognises that doubles the input string and concatenates the invert of the input

I have to design a Turing machine which takes a input string $a^{*}$. $a^{*} = \left \{0,1 \right \}^{+}$ Following this pattern where S is the input string: $$ S_{n} = \left \{0, n=0 \right \} \\ \\...
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In a rigorous mathematical sense, what is the significance of Turing-completeness?

I know that Turing-completeness is the ability to simulate a Turing machine, and from what I've read, the reason why we should care about Turing-completeness is that it demonstrates that a machine can ...
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Why is a Language L(M) {has at least 10 strings} turing recognizable and L(N) {has at most 10 strings} is not?

Why is a Language L(M) {has at least 10 strings} recognizable and L(N) {has at most 10 strings} is not? ...
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kolmogorov complexity for finite Language?

In lectures my professor proved that there is no Turing machine that for every x it calculates k(x). On the other hand, I saw a claim online that for finite language L there is a Turing machine that ...
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Finite Number of Turing Machines that stop after k steps?

For this question suppose Alphabet for input is {0,1}. Given: L={<M> | M stops on every input after maximum 1000 steps} My professor claimed that there is a ...
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Is the language of PSPACE Turing Machines decidable?

Let $$L_{\text{PSPACE}}=\{\langle M\rangle : M \text{ is a TM using a polyspace amount of memory}\}$$ Is $L_{\text{PSPACE}}$ decidable? I don't think we can use Rice's Theorem because this doesn't ...
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Definition a Turing machine (which may or may not halt) as a function... notation?

I would like to define a Turing machine as follows. Let Z be an alphabet, and let L be the set of all sentences of this alphabet. For instance, Z={0,1}, then L is the set of all binary sentences. A ...
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Is the set of all halting programs for all universal Turing machines recursively enumerable?

I understand that one can use dovetailing to recursively enumerate the domain of a UTM. However, I am trying to recursively enumerate the domain of all possible UTM. My starting point was to use a ...
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How Turing Machine Can Never Stop?

My professor discussed the following Turing machine M' on input (,x): Generate number n Run M on X, for n steps If M stops, accept I don't understand No.3 If we are running M on input X for final ...
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Are all Turing machines Turing complete?

I have recently been reading up on TOC, and had this thought, which does not seem to be answered explicitly anywhere. They way I have understood it, a system is Turing complete if it can simulate any ...
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Confused about Turing Recognizability

If Turing Recognizability means a T.M. will either halt on input w if w is in the language, or run forever if w is not in the language. How can we know the language is Turing Recognizable if we run ...
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Undecidability of a set of Turing Machines

Considering the following set, I have to say if it is undecidable, decidable or semidecidable: $$S_1 = \{y | \forall n \text{ the Turing Machine } M_y \text{ does not accept any string of length } n\}$...
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Design a two-tape deterministic Turing machine M that recognizes the language L3= {x#(0^k) #y : x, y ∈ {0, 1}* , x = y ∧ |x| = k}

I'm having a hard time trying to write a two tape Turing machine I wanted to first think Oh all I'd have to do is scan from left-to-right till I find the strings that matches the accepted strings) ...
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How is the time complexity of a non-deterministic Turing machine defined?

I read different things online about this: In Sipser, p. 283. The time-complexity of a NTM is defined as the maximum number of steps it uses on any branch on any input of length n. So this is only ...
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What does c represent in Sipser's explanation of the modified post correspondence problem Introduction to the Theory of Computation book?

I'm supposed to perform actions corresponding to the different steps in Sipser's explanation of the Modified Post Correspondence Problem, but I'm not sure I understand the third step. The part I'm ...
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Showing Turing machines are more computationally powerful than Finite State Machines

I've been pondering on whether Finite State Machines, particularly Mealy machines, can describe any computable function as Turing machines do. However "Mealy-computability" does not seem to ...
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Turing Machine that accepts L(M1) = {x^n y^2n z^n | n ∈ N}

I'm trying to design a Turing machine that accepts all strings in the language $$\{x^{n}y^{2n}z^{n}|\ n\in N\}$$ but I'm having trouble getting it to accepts when n> 1, for some reason it rejects ...
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Proving set of register machines that halt before k steps for some input is non-recursive

Given an enumeration of register machines $R_n$ that take a single natural number as input, and a constant $k$, the function $f$ is defined as: $$ f(n) = \begin{cases} 1 & \exists m \text{ such ...
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How it's possible decide CNF by having a turing machine that decide SAT?

Suppose we have a Turing machine $M$ as black box that decide $SAT$ problem. Now suppse we have a $CNF$ formula $\phi$ with $n$ variables. How it possible checking satisfiblity of $\phi$ and then ...
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Is there any problems with equating Turing Machines with Algorithms and Language with Problems?

In a lot of the online explanation of complexity theory, the author proposes the following. "The definition associated with complexity theory (e.g., definition of NP) is phrased in terms of ...
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Turing machine accepting square

I'm trying to figure out following assignment and I could use your help, because I'm stuck. Task: Construct a Turing machine accepting words in format $1^k$, where $k=n^2$, $n$ being an integer. ...
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Is the language containing Turing machine $(M_1, M_2)$ such that $L(M_1) \cup L(M_2) = \Sigma^*$ decidable?

We are given two Turing machines $M_1$ and $M_2$ and we wish to decide whether the union of the language $L(M_1)$ accepted by $M_1$ with the language $L(M_2)$ accepted by $M_2$ coincides with $\Sigma^...
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What is the point of encoding universal turing machines?

I am unable to understand why do we need to encode turing machine at all? I heard that we are trying to build a programmeable turing machine but can't relate how encoding it will make this ...
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A turing machine L takes a machine <M> which has to halt at for least n Inputs

I've been wondering about this problem for a while: Say we have L = { <M>, n | M has to halt for at least n Inputs} and multitapes are simulating various inputs bla bla How do I count how many ...
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Halting problem is undecidable proof-:

Confused with this proof. I will point my confusions here. what is R(M)? They say it is representation of turing machine but what is it exactly? Is it tuples of turing machine? How do we decide w is ...
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A query regarding equivalence of Parallel vs. Serial cells Turning Machine

Given: A Turing machine (set of programs) that behaves as follows: It has some fixed number of states $(S)$ and binary alphabet $(0/1)$. For some constants $k, p, (k<N, p< N)$: Its read/write ...
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What happens to a Turing Machine if it enters final state but the input is not yet read completely?

In the image, the language of the TM is defined on (a, b, c, d) and there is no transition on final state, but strings consisting of d are also part of the language. In all TM problems I have seen ...

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