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

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An Undecidable but not Universal Turing Machine?

I have seen many examples of universal Turing machines, all of which are undecidable due to the undecidability of the halting problem. I have also seen proofs that certain really small Turing ...
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0answers
12 views

Proof of theorem about connection between nondeterministic and deterministic Turing machines complexity classes

I need source for proof of this theorem: Every $T(n)$ time nondeterministic Turing machine has an equivalent $2^{O(T(n))}$ deterministic Turing machine. I have book by Michel Sipser, ...
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1answer
29 views

Prove language is in $NP$ without using a reduction

I've been stuck on this question for hours, can't seem to figure this out. $L = \{\langle M, x, y \rangle\ |\ M$ is a non-deterministic Turing machine over $\{0,1\}$ and $x,y \in \{0,1\}^*$ and ...
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0answers
69 views

UPPER bounds of the busy beaver function?

I learned that the busy beaver function grows very rapidely indeed. The first 4 values are known. I would like to know if there is any UPPER bound known for $$\Sigma(n)$$ for some $n\ge 5$. ...
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0answers
43 views

A Turing machine that can read and determine if another turing machine is valid

Hey I have to write a turing program that will read in another turing program and determine if it is a valid turing program. The program to be read in would have each of its states represented by IO, ...
0
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1answer
13 views

path of non-deterministic and deterministic turing machines

So let's say that we have state 1 2 and 3. In both the non-deterministic and the deterministic turing machine, we only have one-way transitions between the state 1, 2 and 3. For example, if we can go ...
2
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1answer
31 views

What's the difference between a non-deterministic turing machine and a deterministic turing machine?

From what I understood, it seems that the difference is that a NTM can have 2 inputs for which there is a different output or direction. For example, state A for input 1 can result in output 0 and ...
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2answers
137 views

Milton Green's lower bounds of the busy beaver function

Wikipedia states that Milton Green demonstrated in 1964, that the busy beaver function $\Sigma(n)$ has the lower bound $$\Sigma(2k)>3\uparrow^{k-2}3$$ I read the talk about the busy beaver ...
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1answer
434 views

Build a deterministic turing machine to decide L = { ww }

As the title says. w is in {a, b}^*.Note that I am not looking for the non-deterministic one. Use a Turing machine of one tape and "pointer". An idea: I thought that I would do something like ...
1
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1answer
34 views

Recursively Enumerable Languages and Turing Machines

L1 = { M | Turing Machine M terminates for at least 637 inputs} L2 = { M | Turing Machine M terminates for at most 636 inputs} One of them is recursively enumerable, which one?
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1answer
39 views

Showing a Problem Is Undecidable

How can I show that T is undecidable using only this information? $$T = \{\langle M, w, r\rangle \mid M \text{ accepts } w^r \text{ when it accepts } w.\}$$ So, what it's saying is that the machine ...
0
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1answer
59 views

Accepting/rejecting states in Turing Machine

In language decidability problems, a TM halts with a halting state, an accepting state or a rejecting state. My understanding is that when a TM machines halts on accepting state, it removes everything ...
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0answers
75 views

A turing machine which computes the same language as a “stay put” turing machine

Im not sure I really understand how stay put machines work. I know they are just like turing machines but with states. So they can "stay put". But what confuses me is when you define a FSA for a ...
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2answers
65 views

Decidability of Recursively Enumerable Languages

I'm having trouble with this problem, I know that every decidable language is recursively enumerable but that not every recursively enumerable language is decidable. What are the steps involved in ...
0
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1answer
37 views

Turing Machines and Decidability

I saw this question in a textbook on decidable languages, and I was wondering how you would go about solving this type of question: Assume L1 and L2 are decidable languages. Which of the following ...
1
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1answer
62 views

Show that the Turing machine will solve the self-halting problem

Suppose we have Turing machine $M^*$ that: i. halts printing 1 if $M_n$ halts on input 1 ii. halts printing 0 if $M_n$ doesn't halt on input 1 Show that you cannot construct $M^*$. ...
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1answer
39 views

Proof that such a Turing machine cannot be constructed…

Prove there can be no Turing machine $M^*$ that takes input $n$ and: i. halts printing 1 if $M_n$ halts on input 1 ii. halts printing 0 if $M_n$ doesn't halt on input 1 Intuitively I can see why ...
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1answer
29 views

What is the Church-Turing thesis?

Every source I look at online says something vague about Church's notion being equivalent to Turing's, but what exactly is the Church-Turing thesis? As I understand, it attempts to precisely define ...
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1answer
54 views

Prove $L$ = $\{\langle M \rangle$ | $M$ is a TM over $\{0,1\}$ and $\langle M \rangle \langle M \rangle \notin \mathcal{L}(M)\}$ is undecidable.

Was stuck on this for a bit so I need to know if I am on the right track. To show that $L$ is undecidable we will show that $\overline{L}$ is undecidable instead. Suppose $\overline{L}$ is decidable ...
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3answers
70 views

How does one generally use partial function in logical statements?

How does one generally use partial function in logical statements? How it's done in practice? Specifically, let $M$ by a Turing machine, $f_M:\{0,1\}^*\to\{0,1\}$ the characteristic function which ...
2
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1answer
52 views

Are all constrtuctively describable functions continuous? Do they necessarily come with a topology?

In the paper "An injection from $\mathbb{N}^\mathbb{N}$ to $\mathbb{N}$" by @AndrejBauer, about the question whether there exists an injection $\mathbb{N}^\mathbb{N}\to\mathbb{N}$, we writes ...
2
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0answers
73 views

Prove that $\overline{L}$ is not recognizable by showing that $B_{TM} \le_m L$

$\textbf{Problem}:$ $L$ = $\{\langle M \rangle$ | $M$ is a Turing machine over $\{0, 1\}$ such that for some $x \in \{0,1\}^*$, $M$ does not halt on input $x\}$. $B_{TM}$ = $\{ \langle M \rangle$ | ...
0
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2answers
70 views

Turing machine true/false questions

There is a non-regular language that is recognized by a Turing Machine. I believe the answer to this is true, because Turing machines can "count" computations and ...
1
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1answer
75 views

Let $L_{UIUC}$ = $\{ \langle M \rangle$ : $L(M)$ contains the string $UIUC\}$. Prove that $L_{UIUC}$ is undecidable.

Been stumped as to why the following proof works. Note: I have taken this proof directly from here. Proof by reduction from $A_{TM}$. Suppose that $L_{UIUC}$ were decidable and let $R$ be a Turing ...
0
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1answer
74 views

What does it mean for a Turing machine $M$ to accept $\epsilon$

Suppose $B_{TM}$ = $\{ \langle M \rangle$ | $M$ is a Turing machine over $\{0, 1\}$ and $M$ accepts $\epsilon\}$. I do not understand what it means for $M$ to accept $\epsilon$. Can someone explain ...
3
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0answers
122 views

Proving a language is not recognizable

I have the following question that I just want to verify I have done correctly. Let $L$, $L_1$, $L_2$ $\subseteq \Sigma^*$ such that $L = L_1 \cup L_2$, and $L_2$ is decidable. Prove that if $L$ is ...
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0answers
238 views

A turing machine for binary addition

How would I write a turing machine which has configurations which does 2 bit binary addition?
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2answers
69 views

The halting problem for tapes that are or are not completely blank

Is it possible to construct a Turing machine that halts only if the tape is not completely blank? Also, is it possible to construct one to halt if the tape is completely blank? Intuitively, I think ...
2
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1answer
85 views

Designing a turing machine

Suppose you have a tape that has a block of $a$ strokes followed by a space, followed by a block of $b$ strokes, followed by a space, followed by a block of $c$ strokes, and otherwise blank. ...
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1answer
90 views

If $L_1 \cap L_2$ is decidable, prove/disprove that $L_1$ and/or $L_2$ are decidable

Question: Let $L_1$ and $L_2$ be languages over the alphabet $\Sigma$. If $L_1 \cap L_2$ is decidable, then $L_1$ is decidable or $L_2$ is decidable (or they both are). Definition of a decidable ...
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1answer
25 views

Interpreting probabilistic time turning machines

I was trying to understand better the definition of a strong PSRG and I came across this expression which I am trying to understand better: $$ Pr_{r \in \{0,1\}^l}[A(r) = "yes"]$$ Where r is a truly ...
2
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1answer
135 views

Number of possible configurations in a Turing Machine

While studying for an up-and-coming exam, I stumbled upon the following question: $$ L=\{\langle M \rangle,\langle w\rangle:M\text{ is single-tape and }M \text{ running on }w \text{ doesn't go over ...
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1answer
37 views

Languages in P that are not P-complete

Why aren't there any languages in P that are not P-complete?
2
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1answer
61 views

Prove that RE is closed under reduction

Prove that the class RE is closed under reduction. Definitions: A language $ A \subseteq \Sigma^*$ is called reducible to $ B \subseteq \Gamma^*$ ( denoted by $A \leq B$) if there is a computable ...
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1answer
37 views

Languages that are not comparable in $R$

I want to know if there are $2$ languages $A,B\in{R}$ such that there's no reduction between them. Namely, $2$ languages $A$ and $B$ $\in$ $R$ such that $A\not\le B$ and $B\not\le A$ Thanks a lot!
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1answer
197 views

prove Turing recognizable

This is actually an old exam question its not my homework; Let L = { : M is a TM with an input alphabet of {a,b} and M accepts at most one word, i.e. M either accepts no words or accepts exactly one ...
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0answers
45 views

Extended PDA vs TM

We studied in class that PDA is less powerful than TM. My question is: Extended PDA : for every $\alpha,\beta \in \Gamma \cup \{\epsilon\}$, $\sigma \in \Sigma \cup \{\epsilon\}$, $q,r \in Q$, $w ...
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0answers
23 views

reverse of language, decidability

Consider a language L(D) = {w: w and its reverse are in L(D)}. Does reverse of L(D) is the same language ? If so, then consider L = {: M is a DFA for L(D)}, does this make this a turing decidable ...
2
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1answer
48 views

Given a single taped deterministic turing machine what's the least amount of calculations needed in order to receive the language

Given a single taped deterministic turing machine what's the least amount of calculations needed in order to receive the language $L_k=${$0,1$}$^*0${$0,1$}$^{k-1}$. My intuition says that i'll need ...
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1answer
79 views

Solving the halting problem for *almost* all machines?

As I understand it, the proof of the halting problem’s undecidability is conceptually pretty simple. You postulate a machine $h(m, x)$ which (1) always halts and (2) returns 1 if $m$ halts with input ...
2
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1answer
54 views

Concrete universal turing machine

I read about universal turing machines in the internet, but I did not find a concrete listing of a universal turing machine and a descreption, how a specific turing machine has to be coded that the ...
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0answers
91 views

Oracle Turing machine - $E_{\text{TM}}$ and $PCP$.

$$E_{\text{TM}}=\{\langle M\rangle|M\text{ is a TM and $L(M)=\emptyset$}\}.$$ $E_{\text{TM}}$ is undecidable $$PCP=\{\langle P\rangle|P\text{ is an instance of the Post Correspondence Problem with a ...
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1answer
53 views

Reducing A$_\text{TM}$ to REGULAR$_\text{TM}$

We can solve A$_\text{TM}$ problem using REGULAR$_\text{TM}$. Assume $R$ is a Turing machine that decides REGULAR$_\text{TM}$. We construct $S$ to decide A$_\text{TM}$ as follows On input ...
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1answer
46 views

Assign Integer to Each Turing Machine

I have the following problem: suppose that we have an infinite set of symbols, $A = \{a_1, a_2, ...\}$ from which all Turing Machine input alphabets are chosen. Show how we could assign an integer to ...
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0answers
63 views

Blanks in the Tape of a Turing Machine

I used to have a lot of trouble with Turing Machines, primarily because I thought that in-between input symbols on the tape, one could have an arbitrary number of blanks, so every input would need to ...
2
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1answer
101 views

Turing Machine for comparing, copying, and operating

If one wants to design a Turing Machine for a function such as this: Where $x>0,y>0$ and are both integers represented in unary, so an example movement in this TM on the read-write head would ...
2
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1answer
264 views

Show that the language TOT={<M> | M is a Turing Machine that halts with all inputs} is not recursively enumerable nor its complement.

I've been thinking about how to show this but I'm stuck. I'm required to prove this: "Show that the language TOT={#M# | M is a Turing Machine that halts with all inputs} is not recursively ...
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1answer
45 views

Computably enumerable and partial functions

I've been tasked with proving, formally or informally, that these conditions of a language A which is a subset of {0,1}* are equivalent statements. I must first show that A itself is computably ...
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0answers
68 views

Primitive recursive and Turing machines

Can someone give me a hint or the start of a possible proof for the following theorem: A function $f: \mathbb{N}^r \rightarrow \mathbb{N}$ is primitive recursive if and only if there is a ...
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47 views

(2,5) Turing Machine implemented with chess pieces

I recently came across a (limited) reference to a (2,5) Turing machine implementation that can be represented using chess pieces on a 2D board. I know it is possible to implement a UTM using ...