Questions tagged [decidability]

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The role of diagonalization - asymmetry between TM and Recursion Theory

This might be a slightly strange or irrelevant question. My apologies if it is. I'll try to formulate it the best I can. First, here is an hypothesis: diagonalization is syatematically used to prove ...
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Effectively decidable vs. noneffectively (or ineffectively) decidable

The introduction of https://www.sciencedirect.com/science/article/pii/0001870882900482 starts with the following sentence: The word problem for commutative semigroups is effectively decidable. I ...
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Prove that { $\langle M \rangle$ : $M$ is a TM and $L(M)$ is decidable} is undecidable

So I want to prove that $$ \big\{\langle M \rangle : \text{ M is a TM and } L(M) \text{ is decidable} \big\}$$ is undecidable. To do so I want to reduce it from$\ \overline{A_{TM}}$ with a function ...
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Decidability of $\{⟨G⟩ \mid \text{$G$ is CFG and $L(G) ⊈ \Sigma^+$}\}$

I want to prove that the following language is decidable: $$\mathit{SEQ}_{\mathit{CFG}} = \{⟨G⟩ \mid \text{$G$ is CFG and $L(G) ⊈ L$}\}, \text{ where } L = \Sigma^* - \{\epsilon\}$$ So, I think about ...