Recursive language and non recursive enumerable language : Doubt

Question

I have following doubt

1. FA , CFG and CSG are recursive

2. Type 0 language is recursive enumerable

3. Recursive means if let L is language and w is a string , if we put a string into Turing machine so it will accept if it is belong to it or reject when it is not belong to it  .

4.  Recursive Enumerable means if let L is language and w is a string , if we put a string into Turing machine so it will accept if it is belong to it and go to loop if it not belong to it .

Are these things right ?

Comments

Just make small modifications

Type 0 languages are Rec as well as RE

For RE it can accept the string if it belongs to it but can halt or can’t halt we can not say. I mean we can’t say it might go into infinite loop. That string might get accepted.

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Type 0 Grammars are unrestricted grammar or RE.

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@Ashwin I don't think so it is not Recursive it is Recursive Enumerable becoz Recursive is proper subset of Recursive Enumerable viceversa  is not allowed .

Answer 1

1&2) Regular grammar ⊂ CFG ⊂ CSG ⊂ Unrestricted grammar

The set of grammars corresponding to recursive languages is not a member of Chomsky hierarchy, these would be properly between Type-0 and Type-1.

3&4) https://gateoverflow.in/108404/self-doubt

Answer 2

1,2,3 are correct but in last one something missing

Recursive Enumerable means if let L is language and w is a string , if we put a string into Turing machine so it will accept if it is belong to it and if string not belongs to it, turing machine will either reject or go to infinite loop