When is a problem said to be decidable or undecidable?

[shivajikobardan]

Definition 1-:https://lh6.googleusercontent.com/mKVgfAdOOXQUjpsgw5h2pGNfVLLZHC8ZEZ3up_Gtxosm_TrMaYWg7qPbYhyx72qEwW3z__qp6Ls3fhnPSwDCa9wtGjGqu-i0wn4WVOCCfvoeFuVtnO9lMPSpKZ_Yxs2ORZPLgD6r
Taken from here-: https://research.cs.queensu.ca/home/cisc462/moni/m3.pdf

This in my opinion, just makes things complicated. Decision problem is just something where we get output in the form of yes/no…T/F…etc.
But it says it gives input true or false…can you give me example about that?

I thought the goal of decision algorithm should be to find answer in the form of yes or no.

Definition 2-:
https://lh4.googleusercontent.com/LGJ5Mw19XOGQUgfSwqofQnzI53tDpmI4OPyyQscQ0oGdRPVp1VNNM7xOEqX0uzvN0saBrShn3CYHGUDhxr1qFrfzHcLn1QUn_om-xDpuG41kpy22GTpqUTWkyNAri5g-xJIA46ab
Source-: http://www.cs.virginia.edu/~evans/cs302/classes/class17.pdf

This says something else.

Definition 3-:
https://lh6.googleusercontent.com/SoyiGloVOdLygjH1CcFeh5Hu_KHSr7aFVjQVZj7QNdi9JXsshYGXaIz6bVJ-ahW4B9kB7ji7DeDgLS5uWnHj3Ek6ykZ9EkIDhGTiGQ3QYGzpeB7QKsOqhAdOehkXaKuDIe2ZSDAu

Source-:

This says something else.

I am confused in this seemingly simple thing. What I feel is that “if there is an algorithm to solve it(basically a turing machine) then it is decidable”...else undecidable. Am I right?

 

[Evgeny.Makarov]

This in my opinion, just makes things complicated. Decision problem is just something where we get output in the form of yes/no…T/F…etc.
But it says it gives input true or false

No, the first image does not say this.

This says something else.

No, it says the same thing.

This says something else.

I am not going to watch a 30 minutes video to find that it probably says the same thing.

What I feel is that “if there is an algorithm to solve it(basically a turing machine) then it is decidable”...else undecidable. Am I right?

Yes.