# Questions tagged [semi-decidability]

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### Prove/disprove that the class of decidable (resp. partially decidable) languages is closed under symmetric difference

Prove/disprove that the class of decidable (resp. partially decidable) languages is closed under symmetric difference. A symmetric difference of sets A and B is the set (A \ B) ∪ (B \ A). I know that ...
1answer
71 views

### Which languages, decided by a turing machine are decidable?

How do I decide if a language is decidable and/or semi-decidable? I have theses languages: a) { < M > | L(M) ⊆ 0*} b) { < M > | L(M) contains at least one word of even length} c) {...
1answer
23 views

### Turing Machine equivalence in MinTM proof

The proof with contradiction that $MIN_{\mathrm{TM}}$ is not Turing-recognizable from Michael Sipser's textbook "Introduction to the Theory of Computation" (Theorem 6.7) is as follows: $C=$ "On ...
1answer
51 views

### Is the halting problem undecidable or unrecognizable? [duplicate]

Is the Halting problem in the class of undecidable problems, or it is just in the set of unrecognizable problems? I understand that if it is undecidable, then it is also unrecognizable. I have seen ...
2answers
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1answer
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### Prove Halting on all Inputs is not in RE simulation

I don't understand why when proving if Halting on all inputs problem si not in RE using the complement of the halting problem, I have to take a turing machine and simulate the machine M(the machine ...
1answer
48 views

0answers
216 views

### Decidability of intersection of two languages of same type

Given two context-sensitive languages, $L_1$ and $L_2$ is the problem of "whether $L_1 \cap L_2$ also belongs to CSL" decidable? I have the same question for the case when $L_1$ and $L_2$ belongs to ...
0answers
24 views

### Give an example of a language where both L and ¬L is not semidecidable? [duplicate]

I know ¬H is not semidecidable so I was thinking of creating a language that combines both H and ¬H. Therefore L would be undecidable for ¬H and ¬L would be undecidable for H. Is this a proper ...
0answers
35 views

### Is the language below not decidable , if yes , it is then R.E ?

I am given a Turing machine M as input and i have to find out if this language below decidable and if not is it then in this case recursively enumerable . L=\\\{<M> \mid \text{ is ...
1answer
79 views

### Prove that an infinite set is semidecidible

I have been asked to prove that: Being C an infinite set. Prove that C is semidecidable if and only if exists a total computable function that is injective and whose image is C. I've read the ...
1answer
109 views

### Completeness problem of TM

$L = \{ \langle M \rangle \mid L(M) = \Sigma^∗ \}$ Is above problem R.E ? I found an explanation in one of the websites and I have doubt in few lines of paragraph. The explanation was Now, given a ...
1answer
488 views

### If a problem is “not semi-decidable” and “not decidable” can we say it is “undecidable”?

I was under impression that when a Language (or problem) is not semi-decidable and not decidable then we can say it's undecidable and I think it makes sense also based on diagram. However, in my ...
0answers
153 views

### Turing machine accepts two different strings

I am having hard time to proving this problem $C=\{\langle M \rangle \mid M \text{ is a Turing Machine , } L(M) \text { only contains two different strings}\}$ some ideas that i have tried are : i ...
0answers
79 views

### Decidability of {(M,w); M terminates on input w and tape of M is empty after computation}

I am currently trying to prove whether the above language is decidable, partially decidable or fully undecidable. I am certain that this language is partially decidable and reducible to the halting ...
0answers
54 views

### Prove whether this language is (partially) decidable [duplicate]

I'm currently working on a few turing machine exercises and I can't understand how I can prove whether the below is at least partially decidable: $\{M \mid L(M) = \{x \mid |x| = 10\}\;\}$ where $|x|$ ...
1answer
321 views