given that L is regular, does the following make a context-free language?:

i)${0^x1^y | 0^{x+y} \in L}$

ii)${0^x1^y | 0^{x-y} \in L}$

since L is regular, i presumed that i) can be put into a pushdown automata, but i don't see how to do that for ii). if ii) cannot be put into a pushdown automata, it means it is neither context free nor regular? how can it be shown?

and regarding i) it is a context free, right?

thank you very much for your effort. first post here and i'm glad to join this community

given that L is regular, does the following make a context-free language?:

i) $\{0^x1^y \mid 0^{x+y} \in L\}$

ii) $\{0^x1^y \mid 0^{x-y} \in L\}$

since L is regular, i presumed that i) can be put into a pushdown automata, but i don't see how to do that for ii). if ii) cannot be put into a pushdown automata, it means it is neither context free nor regular? how can it be shown?

and regarding i) it is a context free, right?

thank you very much for your effort. first post here and i'm glad to join this community