Deterministic Pushdown Automata (DPDA) and Deterministic Context-free Languages (DCFLs)
Pushdown automata that we have already defined and discussed are nondeterministic by default, that is , there may be two or more moves involving the same combinations of state, input symbol, and top of the stock, and again, for some state and top of the stock the machine may either read
and input symbol or make an
-
transition (without consuming any input).
In deterministic PDA , there is never a choice of move in any situation. This is handled by preventing the above mentioned two cases as described in the definition below.
Defnition : Let 
be a PDA . Then M is deterministic if and only if both the following conditions are satisfied.
-
has at most one element for any 
and
(this condition prevents multiple choice for any combination of 
) - If
and 
for every 
(This condition prevents the possibility of a choice between a move with or without an input symbol).