Questions tagged [turing-recognizable]
41 questions
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How to show that a function is not computable? How to show a language is not computably enumerable?
I know that there exists a Turing Machine, if a function is computable. Then how to show that the function is not computable or there aren't any Turing Machine for that. Is there anything like a Pumping lemma?
Similarly, how can we show a language…
user5507
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Simple, intuitive example of non recursively enumerable languages
This question is a bit of a shot in the dark. I am asking here, though I am not convinced that such an example exists.
I'd like a quick, highly intuitive example that I can throw out to my students before we engage in the halting problem. I will…
Ben I.
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What are some examples of non-enumerable languages whose complement isn't either?
What are some examples of non-enumerable languages whose complement isn't either? I.e., a language L such that L is not Turning-recognizable and L’ is not Turing-recognizable either.
Update: Found some examples:
Is the below language Non R.E?
HappyFace
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Is the language of Turing machines recognizing regular languages recursively enumerable?
Can we determine whether the following language is recursively enumerable?
$$L = \{\langle M \rangle \mid L(M) \text{ is a regular language}\}$$
Here, $\langle M \rangle$ denotes the encoding of a Turing machine $M$, and $L(M)$ is the language…
Ferran Gonzalez
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How to write a turing machine program for any given problem?
I'm learning about Turing machine program,i want to know how we write a Turing machine program about any given problem, like a string is accepted by Turing machine, program (for a Single Tape Turing Machine) that checks if a binary
number on the…
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Is explicitly explaining the case where the Turing Machine loops forever essential to proving reducibility?
I am asking this in the context of the following question:
Let N be a non-deterministic Turing Machine. We say that N faces a dilemma if at some point in its working, it encounters a situation where the finite control is in the state p, the head…
Aditya
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Prove that the language L = { : T is a Turing machine that runs in polynomial time } is not Turing-recognizeable
By "$T$ runs in polynomial time", I mean that $T$ halts for every input of length $n$ in $O(n^k)$ steps for some $k$.
By Turing-recognizable, I mean that there exists a Turing machine that halts in the accept state iff the input $w = \langle…
jcora
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Is Universality/Completeness Problem of Turing Machines RE or non-RE?
Consider $Universality_{TM} = \{ | \space M \space is \space TM \space and \space L(M)=\sum^{*} \}$
According to Rice Theorem, I know that $Universality_{TM}$ is undecidable.
But is $Universality_{TM}$ Recursively Enumerable or non-RE?
I think…
https_guru
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Is UNIQUE(N) Turing-recognizable?
Let N be a non-deterministic TM with Σ as its alphabet, and we define the next language:
UNIQUE(N) = {w∈Σ*|w has an unique accepting path on N}.
w can have another computational paths on M, but none that result in the accept state.
Is the language…
Dee
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result of a union between a decidable language and not recognizable one - disjoint
I have two infinite languages, A and B, and they're disjoint.
A is not Turing recognizable, and B is decidable.
What's the result of their union? meaning, is it a decidable/recognizable/not recognizable language?
I tried thinking of some examples…
Dee
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set of words w such that M halts on w is decidable
I need to prove that the language following language is not turing-recognizable:
$$\text{dec-haltTM} = \{ \langle M\rangle: \text{$M$ is a TM and the set of words that M halts on is decidable}\}$$
I had the following reduction from…
Dee
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$L=\left \{ \left \langle M,D \right \rangle : M=TM\, ,\, D=DFA\, ,\, L(D)\neq \emptyset\, ,\, L(M)\subseteq L(D)\circ L(D) \right \}\notin RE$
$L=\left \{ \left \langle M,D \right \rangle : M\, is\, a\, TM\, ,\, D\, is\, a\, DFA\, ,\, L(D)\neq \emptyset\, ,\, L(M)\subseteq L(D)\circ L(D) \right \}$
$L\notin R$ which can be shown for example with Turing reduction.
I thought that I build a…
Daniel
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Rice theorem - $EQ_{TM}$
Could use some help understanding if Rice’s theorem applies to the following language: $ = \{\langle \rangle \lvert M \text{ } () \subseteq _{TM} \}$ (where $EQ_{TM} =\{\langle M,N\rangle| M,N \text{ are TMs and } L(M)= L(N)\} $ EQ is in none to…
user169627
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If A U B and A ∩ B are recognizable, then is one of A, A', B, B' also recognizable?
I know that if decidability of $A \cap B$ and $A \cup B$ doesn’t
guarantee the decidability of any of $A$ or $B$. We can prove that:
ATM is not decidable. Since decidable languages are closed under complementation, ATM' is also not decidable. But…
Luis Ramirez
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Proving that $Prefix(L)$ is recursively enumerable
Given a language $L$ that is recursive prove that $Prefix(L) = \{ x \ | \ xv \in L\}$ is recursively enumerable.
My first attempt at this was to try and formulate an algorithm in pseudocode.
Prefix-Recogniser(x)
for v in Σ*:
w = xv
if…
RookieCookie
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