In particular automata theory, pushdown automata (PDA) are abstract devices that recognize context-free languages.

Informally, a pushdown automaton is a finite automaton outfitted with access to a potentially unlimited amount of memory in the form of a single stack. The finite automaton in question is usually a nondeterministic finite state machine (resulting in a nondeterministic pushdown automaton or NPDA) since deterministic pushdown automata cannot recognize all context-free languages.

If we allow a finite automaton access to two stacks instead of just one, we obtain a more powerful device — equivalent in power to a Turing machine. A linear bounded automaton is a device which is more powerful than a pushdown automaton but less so than a Turing machine.

A NPDA W can be defined as a 7-tuple:

W = (Q,Σ,Φ,σ,s,Ω,F) where

• Q is a finite set of states
• Σ is a finite set of the input alphabet
• Φ is a finite set of the stack alphabet
• σ is a finite transition relation
• s is an element of Q the start state
• Ω is the initial stack symbol
• F is subset of Q, consisting of the final states.

There are two possible acceptance criteria: acceptance by empty stack and acceptance by final state. The two are easily shown to be equivalent: a final state can perform a pop loop to get to an empty stack, and a machine can detect an empty stack and enter a final state by detecting a unique symbol pushed by the initial state.

See also

• Stack machine