Pushdown automaton

In computer science, 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 nondeterministic (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: \nwhere

• Q is a finite set of states\n*Σ is a finite set of the input alphabet\n*Φ is a finite set of the stack alphabet\n*σ is a finite transition relation (Q × ( Σ & {ε}) × Φ) × ( Q × Φ^* )\n*s is an element of Q; the start state\n*Ω is the inital stack symbol\n*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.

See also

\n* Stack machine Category:Computational models\n\n\n