Deterministic Pushdown Automata

A nondeterministic finite acceptor differs from a deterministic finite acceptor in two ways:

A nondeterministic pushdown automaton differs from a deterministic pushdown automaton (dpda) in almost the same ways:

The transition function is at most single-valued for a dpda, multi-valued for an npda.
Formally: |(q, a, b)| = 0 or 1,
for every q Q, a {}, and b .
Both npdas and dpdas may have -transitions; but a dpda may have a -transition only if no other transition is possible.
Formally: If (q, , b) ,
then (q, c, b) = for every c .

A deterministic context-free language is a language that can be recognized by a dpda.

The deterministic context-free languages are a proper subset of the context-free languages.