Pushdown Automata

Pushdown Automata

Pushdown automata is an extension of the NFA with $\epsilon$-transitions, it’s essentially an $\epsilon$-NFA with the addtion of a stack.

It recognize all and only the context-free languages.

It cannot recognize non-context-free languages like $\{0^n1^n2^n|n\geq 1\}$(A TM can, however).

Two different versions:

1. Accepts by entering an accepting state.
2. Accepts by emptying its stack.

(Of CFL)

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1. Definition

$$P=(Q, \Sigma, \Gamma, \delta, q_0, Z_0, F)$$
$$\delta(q, a, X) = (p, \gamma),$$
where $X$ is the top of the stack and would be replaced by $\gamma$.

2. Instantaneous Description

$$(q, aw, X\beta) \vdash (p, w, \alpha\beta)$$
$aw$ and here are the remaining input.

3. The Languages of a PDA

4. Equivalence of PDA’s and CFG’s

1. From Grammars to Pushdown Automata

2. From PDA’s to Grammars

5. Deterministic Pushdown Automata