Pushdown Automata

Pushdown Automata

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

It recognize all and only the context-free languages.

It cannot recognize non-context-free languages like {0n1n2n|n≥1}(A TM can, however).

Two different versions:

Accepts by entering an accepting state.

Accepts by emptying its stack.

(Of CFL)

1. Definition

P=(Q,Σ,Γ,δ,q0,Z0,F)

δ(q,a,X)=(p,γ),

where X is the top of the stack and would be replaced by γ.

2. Instantaneous Description

(q,aw,Xβ)⊢(p,w,αβ)

aw and w here are the remaining input.

3. The Languages of a PDA

4. Equivalence of PDA’s and CFG’s

From Grammars to Pushdown Automata

From PDA’s to Grammars

5. Deterministic Pushdown Automata