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edit approved Jun 10, 2020 at 20:25
user122281
edit approved Jun 10, 2020 at 20:25
user122281

A language L is verifiable iff there is a two-place predicate R ⊆ Σ∗ × Σ∗ such that R is computable, and such that for all x ∈ Σ∗: x ∈ L ⇔ there exists y such that R(x, y)

A language is semi-decidable iff there is some Turing machine that accepts every string in L and either rejects or loops on every string not in L.

I've heard that the notion of verifiability can be used to define semi-decidability. How can we show that the class of semi-decidable problems is equivalent to the class of verifiable problems? Or are they not?

A language L is verifiable iff there is a two-place predicate R ⊆ Σ∗ × Σ∗ such that R is computable, and such that for all x ∈ Σ∗: x ∈ L ⇔ there exists y such that R(x, y)

A language is semi-decidable iff there is some Turing machine that accepts every string in L and either rejects or loops on every string not in L.

I've heard that the notion of verifiability can be used to define semi-decidability. How can we show that the class of semi-decidable problems is equivalent to the class of verifiable problems? Or are they not?

A language L is verifiable iff there is a two-place predicate R ⊆ Σ∗ × Σ∗ such that R is computable, and such that for all x ∈ Σ∗: x ∈ L ⇔ there exists y such that R(x, y)

A language is semi-decidable iff there is some Turing machine that accepts every string in L and either rejects or loops on every string not in L.

How can we show that the class of semi-decidable problems is equivalent to the class of verifiable problems? Or are they not?

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DeeDee
DeeDee
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How to prove semi-decidable = verifiable?

A language L is verifiable iff there is a two-place predicate R ⊆ Σ∗ × Σ∗ such that R is computable, and such that for all x ∈ Σ∗: x ∈ L ⇔ there exists y such that R(x, y)

A language is semi-decidable iff there is some Turing machine that accepts every string in L and either rejects or loops on every string not in L.

I've heard that the notion of verifiability can be used to define semi-decidability. How can we show that the class of semi-decidable problems is equivalent to the class of verifiable problems? Or are they not?