1
vote
0answers
25 views

Proof that Finite Turing Machine is reducible to Regular Turing Machine

I know that Finite Turing Machine and Regular Turing Machine are undecidable through Rice's theorem, but I may find a reduction among them? Finite TM = {< M > | L(M) is finite on {a}} Regular TM ...
2
votes
0answers
22 views

Strange Turing Machine 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 ...
9
votes
2answers
169 views

The mother of all undecidable problems

It is usual to show that a problem P is undecidable by showing that the halting problem reduces to P. Is it the case that the halting problem is the mother of all undecidable problems in the sense ...
0
votes
1answer
17 views

Deciding TM which fails to halt whenever the length of its input string is a prime number

I have the following Statement: "A TM called $A$ which fails to halt (i.e runs forever) whenever the length of its input string is a prime number, and eventually halts for all other input strings" ...
0
votes
1answer
25 views

Computable Function and Predicate Question

I See on Our Lecture note on Theory of Computation Course that: .... The basic characteristic of a computable function is that there must be a finite procedure (an algorithm) telling how to compute ...
2
votes
1answer
78 views

Many to one Reducible & Polynomial time

we know that If $A \le_p B$, then $A$ can be reduced to $B$ in polynomial time. we know that If $A \le_m B$, then $A$ is many to one reduction to $B$ . can we deduce that: if $A \le_m B$ then $A ...
-1
votes
1answer
60 views

Recursively enumerable language [closed]

In mathematics, logic and computer science, a formal language is called recursively enumerable (also recognizable, partially decidable, semidecidable or Turing-acceptable) if it is a recursively ...
0
votes
1answer
70 views

$\{x: 2x ∈ M\}$ is R.E Set [closed]

In computability theory, traditionally called recursion theory, a set $S$ of natural numbers is called recursively enumerable, computably enumerable, semidecidable, provable or Turing-recognizable if: ...
2
votes
1answer
87 views

Is it decidable: is there an input for which turing machine will move its head left?

$L=\{\langle M \rangle | M $is a Turing machine and $\exists$ input $x$ such that in $M(x)$ running $M$ moves its head left at least once $\}$ Is $L$ decidable?
0
votes
1answer
52 views

Logic & Computability Problem

i read this sentence in one exam that be false. anyone could say why? if predicate H(x) become false when a program with code r(x) halt on input l(x), then H be a computable predicate.
0
votes
1answer
88 views

Turing & Computability & Computation

We know if we have: we can show (T=t= Turin Redu.) but i have no idea why this relation be correct? any idea?
2
votes
0answers
50 views

Big Challenge in TM & R.E Set [closed]

we know that Halting problem {(M.w) | M halts on input w} is r.e but not recursive. i see the following sentence in one book. "the set of {(M.w) | M halts on input w and M is a TM}} is not r.e" ...
0
votes
0answers
71 views

Primitive Recursive Predicate Challenge

I'm an Computer scientist, and I recently ran into a challenge. If we have primitive recursive predicate $P(x), Q(x)$, I think that all of following 4 expressions can be primitive recursive. Any hint ...
0
votes
0answers
46 views

Recursive Set and Complement Problem

if we have $$A=\{x:|W_x\ne\phi\}$$ can we say always my tight listed below is true? $A$ is recursive , $A$ is r.e, complement of $A$ is r.e, complement of $A$ is not recursive?
0
votes
1answer
73 views

Recursive Set Challenge

we knoe also we know for example if A be any arbitrary r.e set. can we always Necessarily the following is TRUE ? (always) any description is good. (bar sign means complement)
0
votes
1answer
49 views

Complexity & Computation & Logic Problem [closed]

As i study for prepare to CS Final exam, i have some challenges. can i say all of following statements are true? 1) each infinite recursive set, is union of two disjoint infinite recursive set? 2) ...
3
votes
1answer
66 views

A constructive algorithm for a jump of a low set.

Suppose we have an oracle Turing machine which, with $K$ (the halting problem) as an oracle, computes a low set $A$. ($A$ is low if $A'\equiv_T K$) Is there an algorithmic way of obtaining a Turing ...
1
vote
3answers
46 views

Reducing a Decidability Problem to the Halting Problem

Let $L = \{(M, n): M$ halts on less than $n$ elements from a set S $\}$ I'm trying to come up with a generalization on how to solve these types of problems so I have not defined what S is. Since the ...
6
votes
0answers
47 views

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 ...
1
vote
1answer
35 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
votes
0answers
28 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 ...
1
vote
2answers
61 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 ...
1
vote
1answer
57 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 $M^*$. ...
1
vote
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 ...
0
votes
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?
1
vote
1answer
75 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 ...
1
vote
0answers
89 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
votes
1answer
50 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 ...
2
votes
1answer
221 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 ...
0
votes
1answer
44 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 ...
1
vote
0answers
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 ...
1
vote
0answers
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 ...
0
votes
0answers
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 ...
1
vote
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 ...
0
votes
0answers
38 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 ...
-2
votes
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.
1
vote
1answer
105 views

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

I came across these 2 problems about proving of undecidability of languages: $1$. $FINITE_{\text{TM}} = \{\langle M \rangle | M \text{ is a Turing machine and } L(M) \text{ is a finite language} \}$. ...
2
votes
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 ...
0
votes
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 ...
26
votes
4answers
737 views

Why do we believe the Church-Turing Thesis?

The Church-Turing Thesis, which says that the Turing Machine model is at least as powerful as any computer that can be built in practice, seems to be pretty unquestioningly accepted in my exposure to ...
1
vote
2answers
182 views

Decidability and undecidability of a set or language

I want to find out whether the following sets are decidable or not. Generally speaking, what exactly should be done about it? Doing some research, I think a language or set is decidable if a Turing ...
2
votes
1answer
155 views

Injection from computable numbers into natural numbers

Each Turing machine which writes an infinite sequence of 1 and 0 can be regarded as representing a (computable) real number (and of course each Turing machine represents a natural number by its ...
2
votes
1answer
319 views

Is this undecidable language recognizable?

Is this language: $L = \{\langle M\rangle : \text{$M$ is a Turing machine and $L(M)$ is decidable}\}$ which I know that is undecidable, turing-recognizable? Is its complement recognizable? ...
1
vote
2answers
471 views

Turing machine for balancing parentheses on a two letter alphabet

How to construct a Turing machine $M=(Q,\Gamma,b,\Sigma,\delta,q_0,F)$ which decides if a sting on the alphabet $\{(,)\}$ is ''balanced'' (e.g. $(()())$ is balanced and $))(($ or $()(($ is not) with ...
-2
votes
1answer
183 views

Computability of busy-beaver sequence? [closed]

We can draw a parallel between cellular automata and busy-beaver numbers. For example the initial case occupies some kxk square in the plane,leaving all the other cells emty, after how many ...
6
votes
2answers
139 views

Are there known natural problems of intermediate degrees of unsolvability?

I know there exist intermediate degrees of unsolvability, i.e. there are undecidable problems which can be reduced to the Halting Problem, but not vice versa. Are there any "natural" problems known or ...
3
votes
1answer
115 views

Explain why if the language A is recursive, then A is reducible to 0*1*

I'm in a theory of computation class and there is a problem that I think I am way overthinking. Can anyone point me in the right direction with the following: Give a short justification of the fact ...
1
vote
1answer
149 views

The set of Turing machines that recognize $\{00, 01\}$ is undecidable

$L =\big\{\langle T\rangle \mid T\text{ is a Turing machine that recognizes }\{00, 01\}\big\}$. Prove $L$ is undecidable. I am really having difficulties even understanding the reduction to use ...
3
votes
1answer
118 views

Question about $\Sigma_n$-soundness

According to wikipedia (http://en.wikipedia.org/wiki/%CE%A9-consistent_theory#Definition): "$\Sigma_n$-soundness has the following computational interpretation: if the theory proves that a program C ...
1
vote
2answers
174 views

I do not understand why the Turing computable sets of N are exactly the sets at level $\Delta_1^0$ of the arithmetical hierarchy

The reason I don't understand it is this. Take for example the twin primes conjecture, which is $\Pi_2^0$. The set of twin primes is computable right? (there is a Turing machine that enumerates all of ...