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

learn more… | top users | synonyms

1
vote
0answers
14 views

What are the fundamental principles/algorithms on the process of equation solving?

I have seen a lot of solvers that are capable of, for example, getting an equation such as x ^ 2 + x = 12 and finding x = [3, -4]. I know some of them are implemented by hardcoding special cases. For ...
0
votes
0answers
16 views

Difference between Turing machine end state and halt

Is there a difference between the end state of a Turing machine and the halt state? Especially, for example the Busy Beaver 3. It is said that it is with 3 states but there is also a halt. Is the end ...
1
vote
0answers
14 views

Constructing a TM from empty string

Hey I want to construct a deterministic Turing Machine, which out of an empty string tapes six consecutive 1s when halt. I have a question, is it possible to create such without transitions from final ...
-1
votes
0answers
21 views

Prove a TM is decidable [on hold]

When L is a language, length(L) is the language {1^|w| : w ∈ L} ⊆ 1⋆. Let REGLENTM = {⟨M⟩ : M is an TM for which length(L(M)) is regular}. Prove or disprove: REGLENTM is decidable.
0
votes
0answers
33 views

Turing machine from empty string: verification and suggestions

So I must create a Turing machine which records from empty tape six consecutive 1s. I am allowed to use only 3 states. $z_2$ is the final state. Furthermore, it should be deterministic. Here is my ...
-2
votes
1answer
40 views

What is the complement of empty language?

Consider a turing machine that accepts the empty language. What will be the complement of the language generated by the above turing machine? A) Recursive B) Recursive Enumerable C) Non recursive ...
0
votes
1answer
28 views

closure property on languages

The above image, taken from planetmath.org, describes the closure property on REG (regular), DCFL (deterministic context-free), CFL (context-free), CSL (context-sensitive), RC (recursive), RE ...
1
vote
1answer
54 views

Does stay put TM recognizes same languages as standard TM

I am reading this text book and it says that stay put turing machine recognizes the same languages as regular turing machine by just adding transition functions (without adding any new states or ...
1
vote
0answers
39 views

Models of Computation and What they can model [closed]

Some days ago i've discovered that in most of what we call "models of computation ", we can possibly model tasks other than computation itself . For instance, in lambda calculus we can model control ...
0
votes
2answers
38 views

Constructing Turing machines

I get the main ideas of Turing machines. But I can't construct a Turing machine to solve a given question. The question I'm trying to solve is "Construct a Turing machine that recognises the set of ...
-1
votes
0answers
29 views

Constructing a Turing machine for a given language [on hold]

I'm having some trouble with designing turing machines. I do understand what it is and how the operation works, but I don't understand how I would go at building one. When I'm given a task such as ...
7
votes
2answers
61 views

Computability of equality to zero for a simple language

Suppose we have a tree in which leaves are labeled with a set of numbers $L$, and internal nodes with a set of operations $O$. In particular $L$ can be $\mathbb{N}, \mathbb{Z}$ or $\mathbb{Q}$, and ...
3
votes
1answer
21 views

What does $\Sigma^0_2$-hard and $\Pi^0_2$-hard for a TM's Acceptance Problem mean?

I'm reading about a Turing Machine $M$ and it says the problem of deciding whether M accepts a string is "$\Sigma^0_2$-hard and $\Pi^0_2$-hard". I haven't seen this kind of notation before and ...
2
votes
1answer
51 views

Using Generalized Rice's Theorem to Prove Decidability

I have a Turing Machine M with a binary alphabet {1,2} that accepts a language L(M) that has infinitely many strings that start with 1 and finitely many strings that start with 2. I'm trying to ...
2
votes
1answer
140 views

Proving Infinite Turing Machine Language (with finite subset) is Recursively Enumerable

I'm trying to answer this question: Let $S$ be the strings $\langle P \rangle$ accepted by the Turing Machine $P$ with input alphabet $\{a,b\}$, where $P$ accepts an infinite number of strings ...
1
vote
1answer
19 views

Space penalties for the simulation of a non-deterministic Turing machine by a single-tape deterministic Turing machine

If I have some non-deterministic Turing machine $NDTM$ running some process $Q$ and I wish to simulate the same process $Q$ with a deterministic single-tape Turing machine $DTM$, there will of course ...
5
votes
2answers
470 views

Are two non-Turing-recognizable languages closed under union?

If I have two languages that aren't Turing-recognizable, is the union between them always not T-recognizable? Why?
1
vote
1answer
25 views

Are all languages generate by Turing machines countable?

Are all languages generate by Turing machines countable? I know that the set of all TMs are countable, but what about the languages that they generate?
1
vote
2answers
53 views

Turing Machine That Accepts Machines With Undecidable Languages

So I'm reviewing my Computability notes for my final, and I understand how reduction arguments work, but I'm having trouble framing one for the following Turing machine: Undecidable TM = { ⟨M⟩ | L(M) ...
-2
votes
1answer
29 views

How can I construct a Turing Machine that accepts encoding of another Turing Machine? [closed]

How can I construct a Turing Machine that accepts the language L = <'M'> which is an encoding of a Turing Machine M?
0
votes
1answer
36 views

Show that the set of programs whose Kolmorgorov complexity is smaller than their length is recursively enumerable

Define the language $\qquad R = \{x \in \{0,1\}^\ast \mid C(x) \ge |x| \}$ where $C(x)$ is the Kolmorgorov Complexity of $x$ and $|x|$ denotes the length of $x$. Prove that $R$ is ...
3
votes
1answer
35 views

Turing machine working only with 1's and blanks - how to encode input?

Let's say we have a Turing machine which head can only write 1 or blank to the tape (although it can read all symbols from any input alphabet correctly). Can we operate with it on any input? My ...
5
votes
1answer
210 views

How a reduction can help up solve a problem?

I am studying the basics of Computation Theory and I came up with an example I can't understand. Let's have a language $L = \{\langle M\rangle \mid L(M) = \Sigma^{\ast} \}$, so $L$ contains codes of ...
4
votes
6answers
1k views

How is it valid to use oracles in mathematical arguments?

Oracles do not exist. If one did exist, then you would replace them with a subroutine with computational requirements and you would no longer need an "Oracle". Thus, Oracles do not exist almost by ...
1
vote
1answer
52 views

Turing Machine for strings without bbb

I am trying to generate a transition graph for a turing machine that accepts the languages of all strings that do not contain the substring $bbb$ with the input alphabet $\Sigma = \{a, b\}$. When I ...
0
votes
0answers
27 views

Is it decidable whether a TM accepts more than one word?

Is the following language: $\qquad\displaystyle L= \{\langle M\rangle \mid M \text{ is a TM }, |L(M)|>1\}$ Turing-decidable? I think it isn't, because if a Turing machine T can ...
2
votes
2answers
84 views

How to construct a turing machine for a language

I have proved that language $L$ is not regular and think that it is recognizable by a Turing machine. I want to prove it by constructing a Turing machine for it. $L=\{0^n|n \in A\}$ where $A$ is ...
13
votes
6answers
3k views

Is there a physical analogy to the Turing Machine?

Recently in my CS class I've been introduced to the Turing Machine. After the class, I spent over 2 hours trying to figure out what is the relationship between a tape and a machine. I was ...
1
vote
1answer
29 views

Recovering the transition function of a Turing machine with a known number of states

Suppose we have a Turing Machine and know how many states it has as well as bound on its running time, but do not initially know its transition function. Is it possible to determine its transition ...
1
vote
1answer
28 views

Constructing a deterministic one way infinite single tape Turing machine

If I have an input string that is only composed of $a$'s and $b$'s, how can I construct a Turing machine that only accepts strings where the number of $b$'s divides the number of $a$'s? For example: ...
1
vote
1answer
185 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
votes
2answers
472 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 ...
1
vote
1answer
63 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 ...
3
votes
4answers
732 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
votes
1answer
149 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 ...
-1
votes
1answer
31 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 ...
2
votes
1answer
37 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
votes
1answer
25 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 ...
0
votes
2answers
60 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 ...
0
votes
1answer
19 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 ...
0
votes
3answers
54 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 ...
2
votes
0answers
17 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} ...
1
vote
1answer
56 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 ...
1
vote
2answers
27 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
votes
1answer
46 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 ...
-1
votes
1answer
115 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 ...
0
votes
1answer
53 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?
1
vote
1answer
17 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
votes
2answers
62 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 ...
5
votes
1answer
216 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 ...