Formally, we define L(M), the language accepted by final state to be
{ 
| 
for some 
and 
}
2. Acceptance by empty stack (or Null stack) : The PDA M accepts its input 
by empty stack if starting in the start configuration on input , it ever empties the stack w/o pushing anything back on after reading the entire input. Formally, we define N(M), the language accepted by empty stack, to be
{ | 
for some 
}
Note that the set of final states, F is irrelevant in this case and we usually let the F to be the empty set i.e. F = Q .