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
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