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

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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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2answers
79 views

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
18 views

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
52 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
76 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 ...
2
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1answer
25 views

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
54 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 $\phi'(t)=F(t,\...
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1answer
51 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 $\overline{...
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1answer
63 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
67 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 ...
2
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1answer
16 views

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
24 views

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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0answers
37 views

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
50 views

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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0answers
153 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
96 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
74 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
50 views

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 (RNNs)...
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0answers
29 views

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
173 views

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
69 views

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
73 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
79 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
31 views

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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2answers
41 views

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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2answers
34 views

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
61 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
113 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
40 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: #0#...
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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 ?
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1answer
62 views

Show that every finite subset of $\{0,1\}^*$ is recursive [closed]

How can I show that every finite subset of $\{0,1\}^*$ is recursive ?
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1answer
127 views

Read-only Turing machine recognizes only regular languages?

Show that the Turing machines, which have a read only input tape and constant size work tape, recognize precisely the class of regular languages. According to wiki : A read-only Turing machine or ...
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0answers
28 views

Does 3-SAT reduce to 3-CNF-SAT?

I know that SAT goes to 3-SAT and SAT is reducible to CNF-SAT and CNF-SAT is reducible to 3-CNF-SAT but is 3-SAT reducible to 3-CNF-SAT? They are not the same thing though right because cnf makes it ...
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0answers
65 views

Design a Turing Machine to compute the function

I'm tasked with designing a Turing Machine able to run in this Turing machine simulator With the function: f(x) = { x : x < 3 x + 3 : x ≥ 3 Where input: ...
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1answer
65 views

Is a Turing machine on an arbitrary (finite) alphabet equivalent to one on {0, 1}?

Brief context: I'm trying to understand why a Universal Turing Machine exists, on a tape with alphabet $\{0, 1\}$. I think I can see that a $3$-tape Turing machine can represent a Universal Turing ...
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1answer
24 views

State Change in a Turing Machine(Computer of Integer Function)

Im trying to learn how TM can be used as a computer of integer functions. I have this problem The text books gives the construction as follows I understand that intially the R/W head will be ...
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1answer
9 views

Moves in a Turing Machine

In a Turing Machine i understand that δ(q,x) is a transition function that results in a Change in ID. What does δ(q, Xj) =(P, y, L) mean.I understand that L stands for move left.Is P the new state ...
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1answer
17 views

Intersection of Turing Machines Languages

Given a Turing Machine A and a Turing Machine B, how can I know if the intersection of the Languages of both Turing Machines is non empty? L(A) $\cap$ L(B) $\neq$ 0
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1answer
100 views

Proof that a certain language is Turing Decidable

$$L_1 = \{\langle R,S \rangle \mid \text{$R$ and $S$ are regular expressions and }L(R) \subseteq L(S)\}$$ $$L_2 = \{\langle M\rangle\mid \text{$M$ is a DFA that accepts $w^r$ whenever it accepts $w$} ...
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1answer
257 views

Construct a deterministic Turing machine that decides the language $L=\{w\in\{a, b\}\mid w\text{ contains an occurrence of }ab\}$

So we are asked to construct a deterministic Turing machine. I have constructed a Turing machine, but I'm not sure if it's correct. Here is my Turing machine: For the question above, I'm just ...
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2answers
27 views

difference between A* and 2^A*

let A be any input alphabet then what is the difference between A* (kleen closure of A) and 2^A* ?
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1answer
39 views

Prove that the class of Turing Decidable Languages is strictly larger than class of Context Free Languages

Prove that the class of Turing decidable languages is strictly larger than the class of context free languages. (Give a language that is Turing decidable, but which violates the pumping lemma for ...
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1answer
71 views

Draw a Turing machine that recognizes $\{w \in\{0,1\}^*\,|\,w\text{ contains even number of 1's}\}$

Draw a Turing machine that recognizes the language $\{w \in \{0,1\}^*|w \text{ contains even number of 1's}\}$ This is where I am at:
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1answer
46 views

Abstract machines that compute primitive recursive functions

What it the simplest (least powerful) abstract machine that can compute primitive recursive sets, i.e. sets whose characteristic or indicator function is primitive recursive? $$f:\mathbb{N}\...
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1answer
66 views

Language decidability and Post's theorem

I have the following exercise on decidability: Show that the language $L$ is decidable if and only if there exist decidable languages $A$ and $B$ such that $L=\{x\;|\;(\exists y)[\langle x, y\rangle\...
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1answer
42 views

How is $ BPP = BPP_{1/2+n^{-c}}= BPP_{1-2^{n^{-d}}} $

I'm not able to understand how $BPP = BPP_{1/2+n^{-c}}= BPP_{1-2^{n^{-d}}} $ Can any body explain this to me in simple terms. Any help on this is highly appreciated.
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1answer
53 views

Design Turing Machine

Design a single-tape Turing machine with input alphabet {0, 1} to decide the language $$\{ x\in\{0,1\}^* \mid \#(0,x)=2\cdot\#(1,x)\}.$$ Could someone give me clarification on how to approach and ...
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1answer
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Need help in understanding proof “approach” and meaning for “1st order Theory of dense linear orders w/o endpoints is PSPACE complete”

So in my class we are giving a proof for 1st order Theory of dense linear orders w/o endpoints is PSPACE complete. The proof that it is in PSPACE is basically to reduce TQBF. Let $\phi = \exists ...