However, we sometimes choose to omit the "or not a valid encoding" part in order to simplify arguments.

Why doesn't it matter? Checking whether M is a valid TM, D is a valid DFA, G is a valid graph and so on - all of these

"tasks" can be done not only in R but also in P, so you can always "choose to put" the invalid encodings either in

L or in L-bar and it will not really change the correctness of the reduction.

w in L^bar <-> w not in L

in the course we do not always follow this definition, for example, the following language:

{<M>| L(M) contains "012"}

it's complement should be:

L^bar = {<M>| m is not a valid encoding of a TM OR L(M) doesn't contains 012}

while in the course we usually will regard it as:

L^bar = {<M>| L(M) doesn't contains 012}

in some recitations we used the second L^bar while in some other we used the first. also in exams it is usually the second option.

can there be any clarification regarding the exact definition we're excpected to use?

thanks,

Debi.