I have struggle to understand the Rice Theorem.
My understanding of Rice Theorem:
The purpose of this Theorem is to proof that some given language L is undecidable iff the language has a non-trivial propertie.
So, if I want to apply this Theorem I have to show that the following conditions are satisfied:
1) There are two TM's which have the same language and they are either both in the language $L(M_1)=L(M_2)$ or neither is in L ($M_1 \wedge M_2$ are no specific (picked) machines).
2) I have to show that there exists two specific TM's: $M_1'$ which has the property and $M_2'$ which doesn't have the property.
Is this correct?
Perhaps someone can give an example, so that I know how to apply the rice theorem.
What's about the language: $L=${$<M>$|$\emptyset$ $\subseteq$ $L(M)$}
For the first condition:
There are two turing-machine's which have the same language and doesn't accept the language L.
For the second condition:
- $M_1$ is the turing-machine that accepts all, and...
- $M_2$ is the turing-machine that rejects all.
So both conditions are true which implies I can apply the Rice Theorem?
Thank's for your help.