The main reason why acceptance by final state is more powerful than acceptance by empty stack is because the latter requires the ‘PREFIX property’ to be satisfied.
What is prefix property?
It means that no string of a given language is a prefix of other string of the same language i.e. if ‘aax’ belongs to the language then ‘aaxx’ or ‘aaxa’ cannot belong to the same language.
Why is it a problem?
Because since ‘aax’ is accepted by empty stack, therefore while processing ‘aaxx’, the stack will get empty with one ‘x’ left to process. And since we have no rules defined for it, the language will not be accepted.
Why LR(0) is being accepted?
Because LR(0) also requires prefix properties to be satisfied, unlike other LR parser. And therefore DPDA by empty stack can easily process all LR(0) language.
