Questions tagged [turing-machines]

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

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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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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 > ...
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1answer
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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 ...
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70 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
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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
60 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
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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
38 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 ...
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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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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
78 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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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
52 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 ...
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1answer
56 views

Turing machine - compare two words

I have a simple turing machine with single tape. I need to compare two words <w1>$<w2>$ and write output. Language is all letters and numbers. I did ...
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1answer
620 views

Do regular languages belong to Space(1)?

I was wondering, if we take some regular language, will it be in Space(1)? For a regular language X, for instance, we can construct an equivalent NFA that matches strings in the regular language. ...
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1answer
65 views

Computability - The language of all strings of even length

Define a language $L$ as follows: $$L = \{\langle M \rangle \in \{0, 1\}^* | M\text{ is a TM that halts on all strings of even length} \}$$ I can prove that $L$ is not decidable/recursive, but is it ...
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1answer
49 views

Undecidability of emptiness of LBA

How is the emptiness of Linear Bound Automata (LBA) i.e $L = \{B \mid L(B) = \emptyset \}$ is undecidable?
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4answers
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What did Turing mean when saying that “machines cannot give rise to surprises” is due to a fallacy?

I encountered below statement by Alan M. Turing here: "The view that machines cannot give rise to surprises is due, I believe, to a fallacy to which philosophers and mathematicians are ...
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1answer
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Why are those very similar languages in a different complexity class?

i am having a real time understand why the following two languages are in two different complexity classes(the first is NP-Hard and the second is in P). tried to look online at various resources and ...
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0answers
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is this given language in class P? [duplicate]

i was wondering: is this language in class P? $NONDISJOINT_{DFA}\:=\:\left\{<A,B> |\:A\:and\:B\:are\:DFAS\:and\:L\left(A\right)\:\cap L\left(b\right)\:\ne \varnothing \right\}$ explanation: a ...
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1answer
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Proving $L = \{\langle M, w, n \rangle$ : $M$ accepts $w$ within $n$ steps $\}$ is decidable

Show the following problem is decidable: Given $w\in \Sigma^{*}$, $n\in \mathbb{N}$, and a Turing machine $M$, does $M$ on $w$ halt within $n$ steps. My Thoughts: I am new to proving results like ...
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Is reduction from A_TM to EQ_TM possible to prove EQ_TM is undecidable?

\begin{align} EQ_{\mathrm{TM}} &= {\{ \langle M,N\rangle : L(M)=L(N) \}}\\ A_{\mathrm{TM}} &= {\{ \langle M,w\rangle : \textrm{TM $M$ accepts $w$}\}} \end{align} I can do it using $E_{\mathrm{...
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0answers
48 views

Mapping reduction for the useless state problem to prove that its undecidable

I want to give a mapping reduction (many-to-one) using the Empty_TM which accepts nothing, so the accept state is a useless state. This is to show that useless_TM is undecidable. A state q in a TM M ...
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1answer
27 views

Understanding the Linear speedup theorem and how strong it is

Let $k \in \mathbb{N} $ and define the language $L = \{ n,m | n^k = m \}$ Consider a (deterministic) TM deciding $L$ then it has to compute $k$'th power which will take $f(|n|+|m|) + h(k)$ time in ...
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1answer
68 views

How to prove that {<M1, M2> : M1 and M2 are two DFAs and L(M1) $\neq$ L(M2)} is in NL?

My idea is to find a turing machine which recognizes this language in $\log N$ space, could anyone give me some clue on how to find such turing machine?
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1answer
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Construct a decidable set $B$ such that $B \neq A_w$ for any $w \in \Sigma^\star$

I've been stuck on this problem for a while. Any hints would be appreciated! Let $A \subseteq \Sigma^\star$ be decidable. Given $w \in \Sigma^\star$, define $$A_w = \{x \in \Sigma^\star\:|\: \langle ...
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1answer
60 views

Proving $E_{DFA}$ is decidable by running $A_{DFA}$ several times

I am trying to prove that language $E_{DFA}$ is decidable using multiple executions of $A_{DFA}$ (not using the proof in Sipser's book "Introduction to the Theory of Computation"). Can I just use ...
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1answer
383 views

Some basic questions on halt and move in Turing machines

Im trying to learn about and set up Turing Machines (TMs) the simplest ways using the simplest definite rules. I am using my previous knowledge on simple Cellular Automata to do this. I want to write ...
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1answer
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Is turing completeness related to recursive enumerable languages?

I recently came across this term "Turing complete" in my study of morphogenesis models. When I looked up, it said that a turing complete machine can simulate a universal turing machine. When I ...
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1answer
44 views

Finding a mapping reduction from $A_{TM}$ to $\overline{CF_{TM}}$

I am trying to find a mapping reduction from $A_{TM}$ to $\overline{CF_{TM}}$, but I can't seem to find one. Definitions: $$\begin{align*} CF_{TM} &= \left\{ \langle M \rangle \mid \text{$M$ is a ...
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2answers
271 views

Is the language {<p,n> | p and n are natural numbers and there's no prime number in [p,p+n]} belongs to NP class?

I was wondering if the following language belongs to NP class and if its complimentary belongs to NP class: \begin{align} C=\left\{\langle p,n\rangle\mid\right.&\ \left. p \text{ and $n$ are ...
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1answer
19 views

Does $E_{TM}$ accpets the empty word $\varepsilon$?

Let $L = E_{TM} = \left\{ \left<M \right> | M \text{ is a TM and L(M)} = \emptyset \right\}$. Does $L$ accepts the empty word $\varepsilon$? In other words, is $$\varepsilon \in L$$ I'm ...
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0answers
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Is the proof for the undecidability of $A_{TM}$ still valid if we change certain parts?

i have a question based on a question i saw exists on the site, but with wrong information in it and no answer there, so i am reposting it with valid information(cited wrong from the book). on page ...
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1answer
61 views

Turing machine algorithms for $\{0^n1^n\}$ using one and two tapes

I was tasked with finding a way to decide the language $A=\{0^k1^k \mid k\ge 0\}$ in $O(n\log n)$ time, and then to implement it on a deterministic Turing machine with one tape. Additionally, I was ...
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1answer
28 views

Computability - Can a Turing Machine calculate the input's length?

I have looked for an answer for this question which seems trivial, but I didn't find any. Can a Turing machine, given a word $w$, calculate the length of the word?
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Turing Machine Language Class Recognition [duplicate]

Would a Turing Machine that cannot move left, but can move right or stay put recognize only regular languages? And how does it compare to a machine the can do the same, but also move left?
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2answers
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Can a TM recognize whether another TM recognizes a non-empty language?

Let $$L_1 = \{\langle M\rangle\mid M \text{ is a Turing Machine and }L(M)\ne\emptyset\}.$$ Is $L_1$ recognizable? If so, can you give me a pseudo-algorithm? My attempt: I wanted to study ...
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1answer
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Enumerators and recognizers

I got confused by this a bit... the words of any recursively enumerable language $\mathcal{L}_{RE}$ can be enumerated by an enumerator $E$, i.e. there is an effective procedure (using lexicographic ...
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123 views

How to prove the set of Turing machines that accept a string and its mirror is undecidable?

I'm trying to prove the undecidability of the following language. $$L=\{\langle M \rangle\mid M\text{ is a Turing machine and there is a string }w\\\text{ s.t. }M\text{ accepts }w\text{ and }M\text{ ...
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2answers
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Rice's Theorem - usage on $DFA$ or $LBA$

I have read about Rice's Theorem on Sipser's book, and I think I understand it quite well. I understand that it can be used to show that a language is not decidable. However I am not sure about one ...
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3answers
741 views

Fastest algorithm to decide whether a (always halting) TM accepts a general string

Given a TM $M$ that halts on all inputs, and a general string $w$, consider the most trivial algorithm (Call it $A$) to decide whether $M$ accepts $w$: $A$ simply simulates $M$ on $w$ and answer what ...
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3answers
83 views

Are $CF_{TM}$, $\space $ $\overline{CF_{TM}}$ Turing-recognizable?

I have searched the site well through, and also using Google and notes and couldn't find an answer to a question I am wondering about. Given: $$CF_{TM} =\{ \langle M \rangle \mid \text{$M$ is a TM ...
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1answer
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is it possible to reduce $HALT_{TM}$ to $E_{TM}$?

I am wondering, if it is even possible: is it possible to reduce $HALT_{\text{TM}}$ to $E_{\text{TM}}$? $HALT_{\text{TM}}=\{\langle M,w\rangle\mid M\text{ is a }TM\text{ and }M\text{ halts on input }...
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Proving language K is undecidable using the diagonalization method

I have a problem proving the following properties of given language K: $K = \{< M > | M\ accepts < M >\}$ I am trying to prove that language K is Turing-recognizable but undecidable ...
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1answer
189 views

How do I do a subtraction question on turing machine

For example, 111-11 I want to have the output as 111-11=1 I am a beginner at TM and am having a hard time trying to solve this question.
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Turing Machine using finite control memory for distinctness problem

I am building a turing machine that recognizes the following element distinctness problem and I also need the state transition diagram for it, and I just realized after you compare the first two ...