Tagged Questions

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

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1answer
92 views

Show there exists a turing machine with the following properties

I'm struggling to understand a question I've been given. The question asks: Let $\psi$ be a boolean formula in $n$ variables. There are $2^n$ different combinations of assigning values to the ...
2
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2answers
355 views

Turing Machine Decidable: What right does the definition have to say what's not in language L?

I'm having trouble understanding the definition of Turing Decidable. The definition goes something like this: TM M decides language L iff the strings in L put M into the Accept state and the ...
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1answer
49 views

Can a solvable problem be encoded in a recursively enumerable language?

Imagine I have a turing machine that can decide on a specific problem using a language. My question is that that problem (that can be decided by a TM M, with language L) can be encoded in a new ...
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4answers
636 views

What is the point of finite automata?

Why learn finite automata when Turing machines do exactly the same thing? Turing machines accepts the same languages and more so what's the point?
2
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1answer
52 views

Turing recognizable & decidable: binary strings with even length. Let A = {(M) | M is a DFA such that L(M) is not the same as EVEN}

Having trouble with this homework problem. In order to show that A is Turing recognizable and decidable. $\text{EVEN} = \text{binary strings with even length}$ $Let\;A = \{(M) | \,M\; \text{is a DFA ...
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1answer
21 views

Why apply the assumed decide für HALT to the input and its code?

In the lecture notes I have got in class I have the following proof for the halting problem not being recursive Assume $H$ is recursive and TM $M_1$ decides it. Construct $M_2$ that gets ...
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0answers
12 views

Multitape Turing machine with multiple non-blank tapes

A multitape Turing machine is defined to have input only appear on one tape, with the rest of the tapes blank. Are there any formulations of a Turing machine that allow other tapes to be not blank? ...
2
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1answer
23 views

“Print 'em all game” for Turing machines

Suppose that we have a tape restricted to $n$ cells on binaryalphabet $\Sigma = \{0,1\}$ and initially filled with zeroes. We want to build a Turing machine $M_n$ (or better a Linear Bounded ...
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2answers
38 views

Is emptiness of the intersection of the languages of two TMs decidable? [duplicate]

Let $\qquad \mathrm{DISJOINT} = \{ \langle M_1,M_2 \rangle : M_1, M_2 \text{ are TMs and } L(M_1) \cap L(M_2) = \emptyset\}$. How do I know if this language is decidable or not? And How do I prove ...
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1answer
13 views

Definition of Turing machines and rejection states

In some definitions of Turing machine, there is only a set of accepting states and no mention of a set of rejecting states. But it seems to me that the definition that includes only a set of ...
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3answers
48 views

Where does the need for conditionals (if, switch, jump tables, etc…) truly arise? [duplicate]

I know that this question is a bit out-of-the-box, yet i would be glad if someone could help with a good answers for my question because it is something that is troubling my curious mind. When we ...
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0answers
14 views

Simulate NPDAs with DTMs using only polynomial overhead

We know by polynomial-time parsing algorithms like the classical CYK algorithm that $\mathrm{CFL} \subseteq \mathrm{P}$. Furthermore, it is easy to show by direct simulation that $\mathrm{DCFL} ...
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1answer
22 views

Turing-recognizable languages closed under star operation

I'm tasked with demonstrating that the class of Turing-recognizable languages is closed under the operation of star, but I'm confused about how this is true. For example, I have a TM to recognize a ...
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2answers
26 views

Is it necessary to traverse every letter in the tape of a Turing Machine?

Say I want to make a very simple Turing Machine that accepts only strings that contain one or more a's. Can I simply send have the machine move a HALT state once it reads one a, even if there are many ...
3
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1answer
45 views

The language of any constant-time Turing machine is regular

Suppose we have a Turing machine $M$ so that there is a constant $t$ such that the Turing machine always runs in time $t$ or less. Prove that the language of $M$ is regular. This seems to be a ...
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0answers
36 views

Is the following statement true ? If L is a decidable language and L′⊆L, then L′ is also decidable ? Prove your answer is correct [duplicate]

Is the following statement true ? If L is a decidable language and L′⊆L, then L′ is also decidable ? Prove your answer is correct I can't figure out this question. Any tips ?
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1answer
107 views

Proving equivelance of a multijump turing machine and a turing machine

I'm having trouble getting started on this proof, and I was hoping you guys could give me a couple hints/point me in the direction of where to start? Here's the problem: Consider a multijump Turing ...
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0answers
9 views

Are there any recent results regarding Busy Beavers?

It appears there is a lot less research on this subject than around 20 years ago. I was able to find only a few new results (most prominently those displayed by Georgi Georgiev). Did I completely ...
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1answer
36 views

Simulate a regular Turing Machine with one that cannot write blanks

Consider a Turing machine that cannot write blanks. How does one show that such a machine can simulate a standard Turing machine?
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1answer
15 views

Can we obtain a state diagram of a single Turing machine

When illustrating what states are in Turing machine, often the examples of programs, like a checker that checks an input number is even number, are given. But different programs seem to have different ...
2
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2answers
54 views

How is the number of states in a Turing machine bounded?

The definition of Turing machine says that the number of states is finite. However, I do not get how this can be true. Is the number of states in a Turing machine actually not fixed, that is not ...
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0answers
25 views

What is the difference between acceptability,computability,decidability and recognizability in automata theory?

When we say recursively enumerable languages are recognizable and recursive languages are acceptable by turning machine, what is the difference between these two terms? And also what is the meaning of ...
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1answer
16 views

Why are macro tapes bidirectional?

A k-macro Turing machine uses a tape which is split in blocks of k cells and works on all of them directly. After work, the head can end just beside either the right or the left end of such a block. ...
5
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1answer
215 views

Is a secondary TM sufficient to detect all loops?

Procedure: Start a secondary TM in parallel with the first, but have the second perform exactly 1 step each 2 steps the first TM performs (i.e. it runs at half speed). If the second machine ever ...
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2answers
40 views

What is the set of operations of a Turing machine?

From https://en.wikipedia.org/wiki/Abstract_machine A typical abstract machine consists of a definition in terms of input, output, and the set of allowable operations used to turn the former ...
3
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2answers
145 views

Finite number of Turing machines running concurrently on multi-tapes Turing-machine-equivalent?

So basically, there are several (finite number of) Turing machines being able to read off and write to the same set of tapes (the number of tapes is finite, but each tape may have infinite tape ...
1
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1answer
55 views

Are conditionals necessary in computation? [duplicate]

I know this question might seem weird, maybe I'm just overthinking, but this is really troubling me because I've been a computer engineer for some time now and conditionals (if statements for ...
5
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4answers
648 views

Do turing machines assume something infinite at some point?

In a previous question What exactly is an algorithm? , i asked whether having an "algorithm" that returns the value of a function based on an array of precomputed values was an algorithm. One of the ...
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2answers
41 views

Help designing a Turing Machine

I am faced with the following question: Design a Turing Machine that recognizes the language $L = \{1^{2n+1}\mid n \text{ is a non-negative integer}\}$. Show the state diagram. I started doing ...
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1answer
35 views

The meaning of $*$ in regular expressions

I'm designing a Turing machine that decides a language denoted by a regular expression. Let's say this expression is $a^*bbc^*$. Does this machine accept the string $bb$ since $a^*$ and $c^*$ can have ...
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1answer
30 views

Can every recursively enumerable language be defined with regular expression?

Can every recursively enumerable language be defined with regular expression? I came across this question, when studying for my test: Prove that for any finite language $L$, there is a Turing machine ...
2
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1answer
31 views

Is this problem decidable? (computation of $M_1$ longer than $M_2$ on every input)

Is this problem decidable? Given two representations of Turing machines $R(M_1), R(M_2)$, is the length of the computation of $M_1$ longer than the length of the computation of $M_2$ on every input? ...
4
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1answer
45 views

Determining Number of States in a Turing Machine

I am looking at an example Turing machine in my textbook, Automata and Computability by Dexter C. Kozen, and I'm confused as to how they determine the number of states this particular machine has. ...
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1answer
40 views

Proof that L(M) = {accepts the string 1100 } is undecidable

Let $$L_\ = \{\langle M\rangle \mid M \text{ is a Turing Machine that accepts the string 1100}\}\, .$$ To proof that the language $L$ is undecidable I should reduce something to $L$, right? I tried ...
0
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1answer
23 views

Simulating two dimensional tape TM with ordinary two tape TM

So I know that any multiple tape Turing Machine can be simulated with the one tape TM. But what about if we have a two dimensional tape TM? Can it be simulated with the ordinary two tape TM? Will they ...
0
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1answer
91 views

Decidability of a language of Turing Machine descriptions [duplicate]

Given the language $\{ <M> \mid\:$ M is a Turing machine and there is some w ∈ Σ* for which the computation M(w) takes more than 10 transitions$\}$ How can one prove that this ...
3
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1answer
95 views

Non-deterministic Turing machine and palindromes

I have to design a Non-deterministic Turing machine that accepts only non-palindromes in $NTime(n\log n)$. I think this would be easy on a 2-tape DTM. Simply copy the string onto the second tape – ...
3
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0answers
61 views

Problems that provably require quadratic time

I'm looking for examples of problem which has a lower bound of $\Omega(|x|^2$) for input $x$. The problem needs to have the following properties: $\Omega(n^2)$ runtime proof for any algorithm - ...
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1answer
32 views

How to prove strict space lower bounds using crossing sequences in Turing machines?

I understand the notion of crossing sequences when talking about time, however how are they used to actually prove strict lower bounds for some decision/search problems? For example, suppose that you ...
1
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1answer
48 views

Is there a difference between the Bulk Synchronous Parallel Computing model and the Turing Machine [closed]

The Turing model of computing is widely accepted, as a Tape, Head, State register, and a finite state Table to manage transitions. The Bulk Synchronous Parallel Machine model has for its part ...
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0answers
66 views

K -> 2 tape reduction for nondeterministic Turing machines

How to I show that any language in NTIME(T(n)) can be accepted by a non-deterministic 2-tape O(T(n)) time-bounded Turing machine, with modifiable input tape? I've seen the k to 2 tape reduction for ...
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1answer
553 views

What does sublinear space mean for Turing machines?

The problem of deciding whether an input is a palindrome or not has been proved to require $\Omega(\log n)$ space on a Turing machine. However, even storing the input takes space $n$ so doesn't ...
4
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1answer
93 views

Lower space bound on a turing machine accepting palindromes

Let $$ PAL = \lbrace x \in \lbrace 0, 1, \# \rbrace^* | x = rev(x) \rbrace $$ How do I show that a turing machine deciding $PAL$ must use space $\Omega(\log n)$? I have a feeling that I need to use ...
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2answers
97 views

Decidability of empty intersection of two languages accepted by Turing machines

I am really struggling with determining the decidability of languages and cant figure out whether this problem is decidable or not. I have a language $\qquad\displaystyle L = \{ (R(M_1), R(M_2)) ...
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2answers
110 views

Can languages with infinite strings be recursively enumerable?

I am not 100% sure about the definition of recursively enumarable languages. Yes I know how are they defined: There has to exist a Turing machine that accepts all wrods of the language and halts but ...
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2answers
95 views

Is it possible to ever define $L(M)$ of a given Turing Machine, $M$?

In class, we were discussing creating a Turing Machine $M$ based on the set of input strings it should accept, i.e. define a Turing Machine that accepts only the input $\{ w\ \#\ w\ |\ w \in ...
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2answers
87 views

Extension of Rice's theorem

How can one prove that every nontrivial property of pairs of semi-decidable sets is undecidable? (This is an extension of Rice's theorem that "Every nontrivial property of the r.e. sets is ...
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1answer
43 views

How is Rice's theorem applicable to this decision problem?

I recently had a test in introduction to computability and I got the following question wrong. The question Input: A classical Turing machine $M$ with a 2-dimensional tape. output: Does there ...
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2answers
70 views

Does “output” always imply halting in computability?

$L = \{P : P(n)$ outputs $n^2$ for all $n \in N \}$ In questions of this nature, are we supposed to assume that "outputs" means "halts and outputs"? In modern programming languages, I can ...
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2answers
57 views

Strange TM Language on Definition [closed]

i prepare for Autotmata Course Final Exam. in one of lecture, our professor draw this Turing Machine, and wrote DELTA is Neutral element of TM. it'w wrote: Language of this TM is: {$W \in ...