1) I know that turing decidable means recursive language. But does is also means its decidable? So basically i want to know if REC imples decidability and RE implies undecidability or not. I got confused with word decidable in "turing decidable"
2) http://www.geeksforgeeks.org/np-completeness-set-1/ this links says that NP is those decision problems that can be solved by non-deterministic turing machines and P are those problems which can be solved by deterministic turing machines.
So I thought that REC languages are accepted by DTM and RE by NDTM but it turned out that I was false according to this link https://gateoverflow.in/8111/gate2015-2_21 . So that means non-determinism have nothing to do with halting ? and that REC are accepted by DTM and NDTM both ? and also RE also accepted by DTM and NDTM both ?
3) Why we are concerned with DTM and NDTM in P and NP decision problems if we say that DTM and NDTM have same expressive power ? If they have same expressive power why can't we use DTM in NP decision problems?
Thanks for being patient and reading doubt.