This result allows us to prove that A L L P D A ( \\ displaystyle ALL_ ( PDA ) ) is undecidable .
( \\ displaystyle ALL_ ( PDA ) ) is the language of pushdown automata which accept all input .
This result allows us to prove that A L L P D A ( \\ displaystyle ALL_ ( PDA ) ) , the language of pushdown automata which accept all input , is undecidable .