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Questions tagged [recursively-enumerable]

35 questions
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Computability- relationship between R, coRE and RE

I am trying to think of a question that discusses the relationship between RE, coRE and R. Namely- is it true that for all For every language 1∉ RE there exists a language 2∉ coRE such that 1∪2∉R ? I am not sure whether this claim is true or not. I…
IVRODB
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Is L={⟨M⟩∣L(M)∈P}in RE, when P is a non-trivial property and Z∈P is infinite and in RE or R?

Let $Z \subseteq \Sigma^*$ be an infinite language such that $Z \in \text{RE}$ or $Z \in \text{R}$. Let $P \subseteq RE$ be a non-trivial language property Now define the language: $$ L = \{\langle M \rangle \mid L(M) \in P \} $$ Question: If $Z \in…
csmathstudent8
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Good book on (Quantum) Complexity and Computability Theories to start learning the theorem $MIP^* = RE$ as an operator algebraist

I am looking for some greatest references that could help me understand the theorem $MIP^* = RE$ ($MIP*=RE$) step by step. The paper (The Connes Embedding Problem: A guided tour) covers various topics related to this problem, but it is very brief.…
Kadi Harouna Illia
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Reduction from $\mathsf{ALL}_{\mathsf{TM}}$ to it's complement

I'd like to know if there's a reduction $\mathsf{ALL}_{\mathsf{TM}}\leq_{m}\overline{\mathsf{ALL}_{\mathsf{TM}}}$ where of course $\mathsf{ALL}_{\mathsf{TM}}=\left\{ \left\langle M\right\rangle \mid\mathsf{L}\left(M\right)=\Sigma^{*}\right\} $ All…
Ariel Yael
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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 = { ⟨ ⟩ ∣ runs an even number of steps for every input } in RE?

I'm trying to understand the classification of the following language: $$ L = \{ \langle M \rangle \mid M \text{ runs for an even number of steps on every input } w \in \Sigma^* \} $$ That is, the set of Turing machine encodings where the machine…
csmathstudent8
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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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Alternate definition of recursively enumerable languages

Exercise 9.2.3(c) of the book by Hoffman, Motwani, Ullman states In fact a definition of the RE-but-not-recursive languages is that they can be enumerated but not in numerical order How do we show this equivalent to the following definition?…
muser
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Is the problem of "DFA-TM-INCLUSION" recursively enumerable?

Consider the following problem: Input: A Turing Machine M and a DFA D. Question: Is $L(D) \subseteq L(M)$? Of course, this problem is not decidable. Because it is known that judging whether a word belong to a Turing Machine is not decidable. If…
Audra Jacot
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Determine if a given language L is in RE and prove it

Can someone please help me solve this problem? Let $HP = \{ \langle M, w\rangle: \text{$M$ is a Turing machine that halts on input $w$}\}$ denote the halting problem, and consider the language: $$L_2 = \{\langle M \rangle : \text{$M$ is a Turing…
yehr
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Proving Rice's theorem extension

Let a non-trivial $C \subseteq RE$ Prove $\Sigma ^* \notin C \implies L_c \notin RE$ $L_c$ satsifies $L_c=\{\langle M \rangle|L(M) \in C \}$ First of all, I searched this site for over an hour looking for an already written answer so I am sorry if…
MathStudent101
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recursively enumerable and linear bounded automaton

I have a question about linear bounded automaton. Is it false that every recursively enumerable language is recognized by a LBA ? Because LBA has limited tape size so not all recursively enumerable languages can be recognized by an LBA because some…
MathJunior
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function is computable iff its graph is recursively enumerable?

How do I show that a (possibly partial) function is computable iff its graph is recursively enumerable?
empty-search
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Non-Deterministic Turing Machine That Accepts RE-R language

As far as I know for Non-Deterministic Turing Machine (NTM) there are 4 kind of branches: An input is accepted if there is at least one node in the tree that is an accept. An input is rejected if all branches are rejected, which means that it is a…
Yuval
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P NP R RE closures

I wrote the following table for all the closures in those classes. is anything there incorrect? also, would appreciate help with coNP and coRE closures. couldn't find much information about it online.
Skynet
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