REF: https://gateoverflow.in/76419/decidability
Consider the language:
1) L = {<M>| L(M) = $\epsilon$ }
2) L = {<M>| M accepts epsilon }
Now, lets consider the 1st language: It will contain all TM encodings for TM's that accept $\epsilon$.
Now, this is totally undecidable as per Rice's theorem. Should it be interpreted in this way?
Now, this T.M ( highlighted in Red) cant tell anything and hence, its totally undecidable, right?
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Now, the second language contains all turing machine encodings that atleast accept $\epsilon$
Now, if the 1st language is totally undecidable, how come 2nd is RE(but not recursive) since, the 1st language is base for this?
Also, other question is if we can have finite automata that accepts $\epsilon$, then we can also have TM that accepts $\epsilon$, right?