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

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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 $x\}$. $B_{TM}$ = $\{ \langle M \rangle$ | ...
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2answers
68 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 ...
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1answer
67 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 ...
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1answer
68 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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115 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
234 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
65 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
74 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
87 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 ...
1
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1answer
23 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 ...
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1answer
123 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
34 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
59 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!
1
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1answer
163 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
44 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
21 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 ...
1
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1answer
74 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
45 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
88 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 ...
2
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1answer
48 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
44 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 ...
2
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61 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
92 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
216 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
43 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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64 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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0answers
35 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 ...
2
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1answer
38 views

Undecidability of REGULAR_TM

In case you have Sipser's Introduction to the Theory of Computation 3rd edition, I am asking specifically about the proof of theorem 5.3, how the language REGULAR_TM is undecidable. \begin{equation} ...
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11 views

Is the language that consists of machine configurations whose language is a subset of even palindromes semi-decidable?

Let $PAL = \{ww^R\ | w\in\{0,1\}^*\}$. Then let $A = \{\langle M\rangle \ | \textit{M is a Turing Machine and } L(M)\subseteq PAL\}$ Is A semi-decidable (Turing recognizable or recursively ...
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1answer
31 views

Constant value function Turing machine.

How would one go about writing a Turing machine which always computes to a certain value? If the value is small, the problem is trivial of course, but how could I write a Turing machine for the ...
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1answer
45 views

Turing machines and tape complexity

Are the following statements true and/or false? There is a total function $g: \mathbb{N} \rightarrow \mathbb{N}$ so that for each Turing machine $M$ and each natural number $t$ we have: (*) ...
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1answer
77 views

Recursively enumerable language of Turing machines

If you have the language $L_{h}=\{M_{i} | (\exists z \in \sum ^{*}) M_{i}\text{ halts on some input } z\}$ where $M_{i}$ are Turing machines, is $L_{h}$ recursively enumerable? I'm fairly certain ...
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0answers
50 views

Overwriting a blank symbol is semi-decidable

Consider the following language: $$ L = \left\{ \langle M \rangle~ \middle| \begin{array}{c} M \text{ is a single-tape TM that writes a blank symbol $\sqcup$ over a nonblank} \\ \text{symbol during ...
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27 views

Is a sum of an elementary chain on low models low?

We have an elementary chain of low models $(\mathcal{A}_i)_{i\in\omega}$ such that for every $n\in\omega$ the model $\mathcal{A}_{i+1}$ is a model obtained by Low Basis Theorem from the set $A_i$ that ...
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1answer
36 views

Is recursive join of a sequence of low sets also low?

A set $A$ is low when $\deg(A)'\leq 0'$. Suppose we have a sequence of low sets $(A_i)_{i\in\omega}$ such that for every $n\in\omega$ we have $$\deg(\bigoplus_{i<n}A_i)'\leq 0'$$ Let ...
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0answers
56 views

Time constructible, non-time constructible functions

A function T:N→N is time constructible if T(n)≥n and there is a Turing Machine M that computes the function x↦└T(|x|)┘ in time T(n). (└T(|x|)┘ denotes the binary representation of the number ...
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37 views

Proving DIAG2 = $\{\langle M\rangle | \langle M\rangle\langle M\rangle\notin{L(M)}\}$ is not semi-decidable!

This is a homework problem so I don't expect a full solution. I just want a hint on how to do this problem. Just in case you are not familiar with the notation, $\langle{M}\rangle$, means a string ...
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1answer
69 views

How do you argue (or prove) that a certain Turing machine accepts a language?

I have an existing Turing machine that is essentially the same as this one here: X is the blank symbol, # is the end of the tape. The format is input/output, direction. 0 indicates failure ...
5
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1answer
113 views

Lower bounds for bb(7) and bb(8) wanted

The busy beaver function $bb(n)$ is not known for $n \geq 5$. Does Anyone know suitable lower bounds for $bb(7)$ and $bb(8)$? Remark: $bb(6)$ as a trivial lower bound does not count as a suitable ...
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1answer
46 views

Probability over decidable languages

Let $\mathcal S$ be the set of all languages over some finite alphabet $\Sigma$. Prove that the probability of a randomly chosen (arbitrary distribution) language has a decider is zero.
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1answer
102 views

Proof of undecidability of $FINITE_{\text{TM}}$ and $USELESS_{\text{TM}}$

I came across these 2 problems about proving of undecidability of languages: $1$. $FINITE_{\text{TM}} = \{\langle M \rangle | M \text{ is a Turing machine and } L(M) \text{ is a finite language} \}$. ...
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1answer
126 views

Will this Turing machine ever halt?

Consider the following Turing Machine, $T_k(n)$, defined in terms of: $$ T_k(n) = 1 + T_n(n) $$ At a high level, this expression indiviates that we have a Turing machine (with instructions ...
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2answers
62 views

Trying to describe this Turing Machine

Let's say I have the following turing machine: $F_n$ = {M | M is a TM and |L(M) ≤ n} In english, for some given natural number n, $F_n$ is the language of all turing machines that accept no more ...
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1answer
110 views

Why do complex grammars require powerful algorithms?

I am reading a fabulous book on Formal Languages and in the book it says: As the rewrite rules of a grammar become more complex, the algorithm for recognizing the associated language becomes ...
2
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1answer
70 views

Unknown symbol '#' in set

I am reading a text on Complexity theory. There is a set whose notation I cannot understand: "Let $\sum$ = {0,1,#}" From the context, and given that the book is used computer science courses, it ...
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1answer
52 views

problem understanding a solution of Talbot's book (complexity and cryptography)

There's a question which is answered at the end of the book, but I have problem understanding the answer, my own understanding is that its lower bound would be $n^2$ as well. A palindrome is a a ...
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1answer
52 views

the time required to decide $L$

Suppose that a language $L$ is decided in space $S(n)$ by a DTM with alphabet  $\Sigma$ and set of states $\Gamma$. What upper bound can you give for the time required to decide $L$?
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1answer
50 views

Tally method to build a machine (on paper, Turing Machine

Consider function $q$: For any even integer $x\ge0$ (including $0$): $q(x) = 4x$ I want to design a machine (on paper of course) to compute q under the Tally system. Another restriction is that when ...