MHB When is a problem said to be decidable or undecidable?

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The discussion revolves around the definitions of decision problems and their complexities. The initial confusion stems from varying definitions presented in different sources, leading to a debate about the nature of decision algorithms, which are expected to yield yes/no outputs. Participants express frustration over the complexity of the definitions and the inconsistency in how they describe the input and output of decision problems. A consensus emerges that if an algorithm exists to solve a problem, it is considered decidable; otherwise, it is undecidable. This highlights the fundamental distinction between decidable and undecidable problems in computational theory.
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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?
 
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shivajikobardan said:
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.

shivajikobardan said:
This says something else.
No, it says the same thing.

shivajikobardan said:
This says something else.
I am not going to watch a 30 minutes video to find that it probably says the same thing.

shivajikobardan said:
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.
 
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