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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 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:
<math>W=(Q,\Sigma,\Phi,\sigma,s,\Omega,F)<math>
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 (Q × ( Σ & {ε}) × Φ) × ( Q × Φ* )
- s is an element of Q; the start state
- Ω is the inital 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
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