This is related to an assignment, but I would still appreciate help in formalising proof either through private message or on this topic.
The question is about if Rice theorem applies to certain property. For example for a structural property such as number of states. I would argue that:
- The property is decidable through its definition in encoded form.
- The property is irrelevant to the language, because given the same language we can easily find another TM that does not have this property, ie one with empty states, so the property is not a language property, and hence Rice Theorem does not apply, since by definition, Rice theory only applies if it is a non trivial language property.
To me, this seems to be a good argument, but the question is assign a substantial mark of 10, and I feel like this is not enough for 10 marks, am I missing out some rigorous argument that I need to include to make my explanation crystal clear?