Can two different rules be applied at the same step in Type 0 Grammar

Question

As a rule in CFG, we have the liberty of applying any rule for the string S anywhere in the derivation. We can also apply different rule in one step. For example, consider the string S->0S1S and say for example that we have two rules, S->0 and S->1. Then in CFG we can apply both of these & can get 0011 as a result. My question is that is this liberty allowed in Type 0 Grammar also? I am stuck at this point in one of the problems.

Answer 1

Regardless of the type of the grammar, the derivation rules are the same. So, the answer to your question is yes, but...

You should not view the derivation in your example as one step, rather it consists of two steps where you first replace one $S$ and then in the next step the other $S$.

For example, if some of your rules are $Ax \rightarrow y$ and $xB \rightarrow z$, then from $AxB$ you can derive $yB$ (by the first rule) or $Az$ (by the second). But you can not use both rules at once and derive $yz$ (where you would have "used" $x$ twice).