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Informal description

A finite-state machine just looks at the input signal and the current state: it has no stack to work with, and therefore is unable to access previous values of the input. It can only choose a new state, the result of following the transition. A pushdown automaton (PDA) differs from a finite state machine in two ways:

A pushdown automaton reads a given input string from left to right. In each step, it chooses a transition by indexing a table by input symbol, current state, and the symbol at the top of the stack. A pushdown automaton can also manipulate the stack, as part of performing a transition. The manipulation can be to push a particular symbol to the top of the stack, or to pop off the top of the stack. The automaton can alternatively ignore the stack, and leave it as it is.

Put together: Given an input symbol, current state, and stack symbol, the automaton can follow a transition to another state, and optionally manipulate (push or pop) the stack.

If, in every situation, at most one such transition action is possible, then the automaton is called a deterministic pushdown automaton (DPDA). In general, if several actions are possible, then the automaton is called a general, or nondeterministic, PDA. A given input string may drive a nondeterministic pushdown automaton to one of several configuration sequences; if one of them leads to an accepting configuration after reading the complete input string, the latter is said to belong to the language accepted by the automaton.