a pda which can decide on the next transition based also on a "peek" at the element in the bottom of the stack, but it can only do push/pop operation on the element in the top of the stack. is it more powerful than a regular pda or not, that is are there any languages it accepts which aren't cfg's?

try DFA's and NFA's. an NFA has more properties but no more computation power. I have already managed to solve this. not sure why I decided to post here. thanks anyway.