Hi I often have trouble with the notation when having to write the accepted language for a finite automata or CFG. Right know I have a CFG that generates groups of any number of 1's followed by any number of groups of 0's repeated.
$S\rightarrow1A, A\rightarrow0A|1A|0|1$
If I had to guess I would write it as $1(0^n|1^m)^*|n\geq0, m\geq1$, but it just doesnt seem right. Does the kleen star just mean that what is in the brackets can be repeated any number of times or does it also mean the order of the inputs can be changed?
First of all, the grammar you wrore down allows any number of $0$'s and $1$'s in any order, as long as the string starts with a 1. Your regex does not encode this information, so your regex is wrong.
I'm not sure why you are mixing regular expression notation and the "language" notation, but usually people don't combine those.
Note that when you write a regex, the operators allowed are $$( \ ) \ * \ | $$
So, the regex corresponding to your grammar would be
$$R = 1 \ (0 \vert 1) \ (0 \vert 1)^*$$
Since the grammar forces you to have at least one $0$ or $1$ in the $A$ production.
If you are allowed the use of the $+$ operator (which usually stands for one or more occurence, unline $*$ which is zero or more occurence), then your regex can be
$$ R = 1 \ (0 | 1)^+ $$