This type of processing can be represented by an embedded pushdown automaton.

In simpler cases a finite state machine or a pushdown automaton can do the job.

This is where it differs from the nondeterministic pushdown automaton.

For each single pushdown automaton these two languages need to have no relation: they may be equal but usually this is not the case.

The remainder of this article describes the nondeterministic pushdown automaton.

Every context-free grammar can be transformed into an equivalent pushdown automaton.

They are the context-free languages that can be accepted by a deterministic pushdown automaton.

Computations of the pushdown automaton are sequences of steps.

For each pushdown automaton one may construct a context-free grammar such that .

As a result, a visibly pushdown automaton cannot push to and pop from the stack with the same input symbol.

These pushdown automatons were also implemented in minicomputers and microprocessors later, which influenced programming language design.

These languages are exactly all languages that can be recognized by a non-deterministic pushdown automaton.

In order to formalize the semantics of the pushdown automaton a description of the current situation is introduced.

A deterministic pushdown automaton has at most one legal transition for the same combination of input symbol, state, and top stack symbol.

Before reading a particular configuration, the pushdown automaton makes a non-deterministic choice to either ignore the configuration or read it completely onto the stack.

As a result we obtain a single state pushdown automaton, the state here is , accepting the context-free language by empty stack.

This conversion can be used to prove that every context-free language can be accepted by a non-deterministic pushdown automaton.

If the pushdown automaton decides to ignore the configuration, it simply reads and discards it completely and makes the same choice for the next one.

A Turing machine is equivalent to a pushdown automaton that has been made more flexible and concise by relaxing the last-in-first-out requirement of its stack.

The complexity of the program and execution time of a deterministic pushdown automaton is vastly less than that of a nondeterministic one.

The graph-structured stack is an essential part of Tomita's algorithm, where it replaces the usual stack of a pushdown automaton.

A linear bounded automaton is a device which is more powerful than a pushdown automaton but less so than a Turing machine.

The notion of computation of a visibly pushdown automaton is a restriction of the one used for pushdown automata.

Thus the language cannot be accepted by a visibly pushdown automaton for any partition of , however there are pushdown automata accepting this language.

Deterministic pushdown automaton (also abbreviated DPDA)