# Recent questions tagged rice-theorem

1
What is the difference between Non-trivial property (in 1st theorem)and Non-monotonic property ( in 2nd theorem)? I was going through Rice's theorem but unable to differentiate between these 2 properties.Please give the detail to differentiate both For a property to be non-trivial, there ... holding for the language of other (Tno) and L(Tyes)⊂L(Tno) Source: http://gatecse.in/rices-theorem/
2
L={⟨M⟩|TM accepts exactly 154 strings} -------------------------------------------------------------------------------------------------------- this language is not decidable but is this R.E?? by second rice theorem, Tyes ={154 strings} and Tno = more than 154 strings hence, Tyes is subset of Tno.so,it is not even R.E. am i right? please correct me.
3
$L=\left \{ <TM> | TM\ halts\ on\ every\ input\ \right \}$ is above language Recursively enumerable or non recursively enumerable??
Consider the following Languages: $L_{ne}=\{\langle M \rangle \mid L(M)\neq \phi \}$ $L_{e}=\{\langle M \rangle \ \mid L(M)=\phi \}$ where $\langle M \rangle$ denotes encoding of a Turing Machine $M$ Then which of the following is true? (a) $L_{ne}$ ... r.e. (b) Both are not r.e. (c) Both are recursive (d) $L_{e}$ is r.e. but not recursive and $L_{ne}$ is not r.e.