Undecidability means recognizable or unrecognizable

Question

If a problem is undecidable then can we say the problem is either recognizable or unrecognizable

Answer 1

No. It can be recognizable (those whose language is recursively enumerable but not recursive) or unrecognizable (those whose language is not even recursively enumerable).

Comments

Decidability : TM halts(either accepting or rejecting)

yes

Recognizablity : TM halts on accepting only

No, it can halt for reject also just that halting for reject may not happen for all cases.

Undecidablity : which is not decidable it means TM doesn't halt or halts only by accepting

 

This means TM does not halt for some inputs (either accepting or rejecting)

Unrecognizablity : which is not recognizable it means TM doesn't halt

This means TM does not halt for some accepting inputs. (Stronger condition than for the above one).

---

sir, is any difference between Turing unrecognizable languages and Turing co-recognizable languages or both same ?

---

The intersection of a recognizable language and an unrecognizable language is always unrecognizable. Is this statement correct as per the above definitions?

Answer 2

Undecidability only means "Not REC"  now ask yourself does 'Not REC' mean RE ? or not even RE.

Answer it with 'Anything Possible' and here you got it.