TOC RE REC

Question

A RE language can also be called as Turing Recognizable,Turing Acceptable or Turing Enumerable.

And REC can be called as Turing Decidable.

Now When we say that a language is Turing Computable, Strictly what we could say that it is RE or REC?

(Ofcourse if it is REC then it is RE also)

PS : It would be great if you could provide some reliable source for it.

Comments

I think this will help you: http://planetmath.org/turingcomputable 

Read a couple of paragraphs of this wiki page too.

Turing Computable is more of like an extension to Church-Turing thesis. It says that a function $f:\Sigma^{*} \to \Sigma^{*}$ is Turing Computable if there exist properly defined procedure (algorithm) for computing $f(a)$ where $a \epsilon \Sigma^{*}$. 

Now though this is sufficient to make a claim that Turing Computable functions are REC, because there is an algorithm for computing them. I suggest you, to read this thread to understand what really recursive function means. Spoiler alert, they are not functions which call themselves.

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Its not clear what do you want to say,

You are saying Turing Computable means REC?

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Yes. Turing computable languages are REC.

Answer 1

Now When we say that a language is Turing Computable, Strictly what we could say that it is RE or REC?

All Turing computable functions are recursive . That means it is RE .

Read this :

http://www.cogsci.rpi.edu/~heuveb/teaching/Logic/CompLogic/Web/Presentations/Turing-Computable%20Functions%20are%20Recursive.pdf

Comments

Link not active :)

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No, it is active ..

click here 

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Sir amazing pdf !

I searched a lot on net but could not find something which would directly prove Turing Computable implies REC.

Thanks a ton :)