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

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Is the problem decidable with Turing machine M that inputs x,y,z does M halts on these 3 instances

Is the following problem is decidable? Given a Turing machine M inputs x,y,z does M halts on these 3 instances? Hint: make y and z any two artificial inputs that the program stops with these inputs. ...
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23 views

Using reductions of turing machines properly

I recently learned about reductions of Turing machines (here after TM), and here is a solution to a problem using reduction (showing L is undecidable, as defined bellow). I have given the reduction, ...
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2answers
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Construct a turing machine that accepts L = {ww : w belongs to {a,b}*} [on hold]

Construct a Turing machine that accepts $L = \{ww : w \in \{a,b\}^*\}$?
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Is the Antikythera Mechanism Turing-Complete?

Is the following Turing-complete? https://en.wikipedia.org/wiki/Antikythera_mechanism As in, it possible to perform all of the operations of a Turing-machine, albeit with finite memory, with this ...
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simple questions on $TM$s runs lengths

Is it possible that the number of running steps in $TM$ that runs on word $w$ will be $0$? Is it possible that the number of running steps in $TM$ that runs on the empty word $\epsilon$ will be ...
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Prove that a certain intrinsic property of Turing machines is not decidable

Can anyone help me to prove that the following language is nod decidable? $$ A=\{\langle\,M,w,q\,\rangle\mid M \text{ is a $TM$ , $w$ is a word, $q$ is a state in $M$ and while $M$ runs on $w$ it ...
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40 views

Classifying languages

I'm working on understanding what kind of languages are decidable, recognizable, and co-recognizable. I came across this problem that I think will really help me but I'm still quite unsure of how to ...
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1answer
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Is the union of undecidable languages not Turing-recognizable?

The question is as follows: Let us define $$L := \{w \mbox{ | either }w = 1x \mbox{ for some } x \mbox{ ∈ $A_{TM}$ or } \mbox{$w$ = 0$y$ for some $y$ ∈ $\overline {A_{TM}}$}\}.$$Prove that neither ...
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Prove uncountability of set L that L and L' neither of which is recursively enumerable.

How do I prove that the set of all languages L on alphabet {0,1} that neither L or L' are recursively enumerable, is uncountable? Proving uncountability can be done through diagonalization like the ...
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1answer
32 views

proof that languages are/are not in RE (probably with mapping reduce)

Given $2$ languages: Let $u \in \Sigma^*$ (constant word). $A_u=\{<M> \big{|}\,\, u\in L(M) \text{ and M is TM }\}$ $B_u=\{<M> \big{|}\,\, L(M)=\{u\} \text{ and M is TM }\}$ I ...
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1answer
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Is each string decideble?

Is it possible to prove that there exist for every string a Turing Machine that decides that string? I think it is provable that for every string you can build a TM that recognises that string, but I ...
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turing machine decidable description for the language

L = { | R is a regular expression that produces at least one word in {a, b} * which contains a symbol exactly 3 times} ...
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1answer
31 views

turing machine decidability language

I must show that this language is decidable but I think it's not {D, Ρ} | D is a DFA and P is a ΡDA which L(D) ∩ L(Ρ) = ∅ } Here what I think I give a reduction from E(TM). I suppose that this ...
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2answers
34 views

Automatic proof verification by a Turing machine

Is it possible to automatically verify a mathematical proof? Or is it proven that this cannot be done by a Turing machine? Thank you very much Kevin
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Turing machine macro notation

This is an example from the book Automata, Computability and Complexity by Elaine Rich. Macro language is defined as follows: (screenshot from the book) And these are the steps mentioned : Scan ...
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0answers
16 views

Prove by printing turing machine that RE closed under iteration

I do not know what is the formal name of printing turing machine in english, maybe "counter machine". This machine prints a whole language without any input. for example: counter machine that counts ...
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1answer
86 views

Prove claims about disjoint union and decidable/undecidable languages

Let $L\subseteq\Sigma^*$ decidable language and $A\subseteq\Sigma^*$. Let $B=A\sqcup L$ (a disjoint union). Prove: $1$. $B\in RE \Rightarrow A\in RE$ $2$. $B\in R \Rightarrow A\in R$ Thanks!
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1answer
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non deterministic turing machine for concatenation

Let $L_1, L_2$ decidable languages on deterministic single-tape TM $M_1$ and $M_2$. How can I build non-deterministic TM that decides $L_1L_2$? What should be the formal definition of $\delta$ (the ...
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1answer
22 views

Drawing a state diagram for a Turing Machine

I'm a bit rusty since it's been a couple weeks since I've last done this, but I could really use some help with starting out the Turing Machine for {a^i b^j c^k | i = j + k} I'm confused on how I can ...
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0answers
20 views

Is there a universal Turing machine on arbitrary number of input variables?

I know that for every $n \geq 1$ there is a partial recursive (p.r.) function $\phi^{(n+1)}_{z_n}(e,x_1,...,x_n)$ such that $\phi_{z_n}^{(n+1)}=\phi_e^{(n)}(x_1,...,x_n)$, where $\phi_e^{(n)}$ is the ...
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Why is it so hard to translate some proves into machine-readable form?

I have just read a topic on mathoverflow about man vs. machine in mathematics. The topic was inspired by the recent victory of Alpha Go over the World Go Champion, Lee Sedol. It reminded me of an ...
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1answer
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Cannot create algorithm for decidable language

L2 = {<M> : M is a TM and there exists an input string w such that M halts within 10 steps on input w} Hi. I am creating an algorithm to show above L2 is ...
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1answer
34 views

Cannot understand solution (Turing Machine & Reduction)

Photo of my problem that I don't understand About question above in photo, I just can't understand its solution provided. We know the complement of Atm = {...
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1answer
61 views

Problems understanding proof of s-m-n Theorem using Church-Turing thesis

I am reading Barry Cooper's Computability Theory and he states the following as the s-m-n theorem: Let $f:\mathbb{N}^2\mapsto\mathbb{N}$ be a (partial) recursive function. Then there exists a ...
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1answer
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Space-Hierarchy Theorem in Theoretical CS

Sipser has a proof this theorem that goes like this: $$D = \text{"On input } w$$ $$1. \text{Let } n \text{ be the length of } w$$ $$2. \text{Compute } f(n) \\ \text{using space constructibility and ...
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1answer
32 views

Which language is decidable

Just been at the Math-exam. One question I was really unsure about, was this question - so I didn't answer it, as you get minus point if the answer is wrong. Does somebody know, what the right answer ...
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1answer
52 views

How is the non-existence of a solution proven?

I've been wondering how an argument that a solution to a particular problem doesn't exist is put together. For instance "Pour-El and Richards found an ordinary differential equation ...
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1answer
40 views

Reduction to/from REC and RE language?

Let $X$ be a recursive language and $Y$ be a recursively enumerable but not recursive language. Let $W$ and $Z$ be two languages such that $\overline{Y}$ reduces to $W$, and $Z$ reduces to ...
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1answer
56 views

Showing set is undecidable with Turing Machines

I'm given the set $T = \{\langle M, w\rangle : M $ is a Turing Machine that accepts $w$ reversed whenever it accepts $w \}$ and I want to show it's undecidable but recognizable. (I'm using the bracket ...
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2answers
55 views

Is there a way to prove that a Turing machine computes the function we designed it to?

Say we design a simple Turing machine that adds two numbers together. Is there any way to formally prove that the machine actually computes the function we 'know' it does? Is there a general method ...
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1answer
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Savitch theorem and its assumption

famous Savitch theorem states: For any function $f\in\Omega(\log(n)), \text{NSPACE}(f(n)) \subseteq > \text{DSPACE}((f(n))^2).$ Why we need an assumption that $f\in\Omega(\log(n))$? Thank ...
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1answer
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Turing recognizable - $B = \{a^n b^n c^n \}$

Question: My answer is no, because it loops forever. But I am a bit unsure if this is the right answer.
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all recursive functions are turing computable

I'm studying with the book computability and logic(boolos). In chapter 5, the theorem is proved, indirectly, by showing that (recursive => abacus) & (abacus=> turing). But I want to prove ...
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0answers
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How are weakly universal Turing machines actually defined?

For what I know, the definition of a universal Turing machine is something along the lines of the following (of course, details might vary from source to source): A Turing machine $M$ is called ...
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74 views

Designing a Turing machine for Binary Division

I'm trying to design a TM to binary divide 2 numbers. The best approach I've found is the method: division as repeated subtraction, but I don't know if there's a fastest way or an easier way. ...
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1answer
95 views

A function given a string ( a program) accepts it if the next program which halts does so in an odd number of steps… is it turing computable

A function which given a string returns 1 if the next program halts with an odd number of steps and 0 otherwise. Is this function computable f(s)=1 if w halts in odd number of steps where w>s and ...
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2answers
72 views

Is this integral less than infinity?

Assume the following integral: $$ \int\limits_{-\infty}^{\infty}\frac{f\left(x\right)} {BB\left(\lceil abs\left(x\right)\rceil\right)}\mathrm{d}x $$ Where $f\left(x\right)$ is any computable ...
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1answer
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Doubt about neural networks that allegedly compute beyond the Turing limit

The question is about a new result by Cabessa & Siegelmann. http://binds.cs.umass.edu/papers/2014_cabessa.pdf : "In this context, we show that the so-called plastic recurrent neural networks ...
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How to compute the solution for this linearized diffusion-reaction system (separation of variables)?

Let $\Omega=(0,a), a>0$ and functions $u(x,t), v(x,t)\in\mathbb{R}$. Consider the diffusion-reaction system $$ \partial_tu=\Delta u+\gamma f(u,v)\text{ for }x\in\Omega,t>0\\\partial_t v=d\Delta ...
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3answers
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Turing Machine divisibility by 6 [closed]

I need to design a TM to check if a binary number can be dividied by 6. I don't know how to design it. Thanks
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2answers
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Have anyone ever thought of continuous analog Turing machine?

Have anyone ever thought of continuous analog Turing machine? The machine adopts continuous (from R) the input data from the tape, It moves to a different state depending on the value on the tape. On ...
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1answer
59 views

Understanding Turing Machines: Recognizable and Decidable langauges

I've searched tons of resources and while conceptually I understand the turing machine itself and what it does- I'm a bit stuck on Turing Recognizable and Turing Decidable languages and I'm not sure ...
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1answer
74 views

There are more languages than programs?

I am reviewing some Turing machine material...and I come across this the set of all programs are countable (convert them into binary string, each of which represent an integer) whereas the set of ...
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1answer
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Deciding set of all Turing machine codes of TMs accepting languages of cardinality $\leq 10$.

Problem: I need to show that the following language is decidable and if not, if $S$ or $\overline{S}$ is partialy decidable language. $S=\{w_e\;|\;|L(M_e)|\leq 10\}$ That is set of all Turing ...
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Unprovable behavior of a turing machine

The wikipedia-article for the P-NP problem [1] says there are three possible answers to the P-NP-problem: $P=NP$ $P\neq NP$ $P=NP$ is independent of ZFC The third possible solution seems to be ...
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Do there exist infinite sets of non-halting programs such that every program in the set computes every other program in the set?

Do there exist infinite sets of non-halting programs such that every program in the set computes every other program in the set, and only programs in that set? I know there exist programs which ...
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1answer
54 views

How to prove whether a language is decidable and/or semi-decidable (or neither) using reduction?

I think I understand the basics of reduction, however I'm far from confident with using the techniques. I have a couple of examples that I'm struggling with: L1 = {< M > | M accepts an infinite ...
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2answers
82 views

Must an algorithm terminate?

I am confused. Sometimes i read about terminating and not terminating algorithms. I almost always read these things in the context of turing machines. This means to me: There are algorithms which ...
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1answer
34 views

How could I design a turing machine that prints all natural numbers on its tape in order?

How one could implement a turing machine that prints all natural numbers of its tape in order. Two consecutive numbers are separated on the tape with the symbol #. The tape should look like this: ...
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How could I modify a Turing machine that attempts to move the head past the leftmost square(crash) on some inputs so that it doesn't crash at all?

Suppose that M is a TM that crashes on some inputs. How would I modify M so that the new machine accepts the same language but does not crash on any input ?