I'm converting a CFG to CNF and there are some details that I'm unsure of. I know the form is
A-->BC
A-->a
Is a transition such as S-->AA|... acceptable? Or do they have to be two different variables?
Is something such as S-->aa|... acceptable? I don't know how to change 'aa' to something else without ending up with AA or aA one of which isn't allowed and the other I'm unsure of.
You are right. There are only two forms of rules in a CNF grammar. Either rewrite a variable into two veriables, or replace it by a single terminal letter.
The rule $S\to AA$ is perfectly OK, the variables can be identical. The rule $S\to aa$ is not OK. You can only generate a single terminal at the time. There is nothing wrong with using an intermediate symbol $A$ and productions $S\to AA$, $A\to a$ as you suggest. It is indeed possible to generate $aA$ but it will not belong to the generated language. The language only contains those generated strings that have no variables.
