P is undecidable and not semidecidable, Q is undecidable and semidecidable and P ⊂ Q

Question

My problem: Define two sets P and Q of words (that is, two problems) such that: P is undecidable and not semidecidable, Q is undecidable and semidecidable and P ⊂ Q

You should ask this at http://cs.stackexchange.com/ or http://math.stackexchange.com/ — runDOSrun, Feb 22 '15 at 17:25

score 0 · Accepted Answer · answered Feb 22 '15 at 17:40

0

One example of such sets:

Define Q as the set of turing machines, which halt on empty input. Define P as the set of turing machines, which halt on every input.

Clearly P ⊂ Q and P is undecidable and not semidecidable, but Q is undecidable and semidecidable.

answered Feb 22 '15 at 17:40

ipsec

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Thanks but why P ⊂ Q ? – Lorenzo J Serranti Feb 22 '15 at 17:59
Because a turing machine, which halts on every input, obviously also halts on empty input. – ipsec Feb 22 '15 at 18:02

P is undecidable and not semidecidable, Q is undecidable and semidecidable and P ⊂ Q

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