self doubt

Question

there is a proof for equivalence of empty stack and final state but what about the prefix property cases empty stack cant accept regular languages which donot accept the prefix property isnt it less powerful than the acceptance by final state ?? what kind of equivalence they have ??

Answer 1

DPDA with empty stack acceptence is Proper subset of DPDA with final state acceptence.

Those DCFLs which don't satisfy prefix property can't have a DPDA with empty stack acceptence.

While in case of NPDA, a NPDA with empty stack acceptence and with final state acceptence both have same powers.

Comments

what is prefix property?

Answer 2

pda with empty stack or pda with final state can accept the cfl without any exception there is no power difference with respect to that

regular languages which satisfies prefix property therefore it is accepted by dpda with empty stack but those violate prefix property can be accepted by dpda with final state only .dcfl  accepted by empty stack is proper subset of the language accepted by dpda with final state