11 - 11: Pushdown Automata Every regular language is a CFL....

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 11: Pushdown Automata Every regular language is a CFL. But some CFLs are nonregular. Since FA ≡ Regular languages, some CFLs cannot be recog- nized by any FA. Examples of CFLs that are nonregular: { a n b n : n ≥ } { ww R : w ∈ { a, b } ∗ } We need to consider a more powerful computation model to rec- ognize CFL – Pushdown Automata (PA). It is an automaton equipped with a stack. a b a Finite control a b a b b b a a Reading head Input Stack 1 Formal definition of PA A pushdown automata is defined as a 6-tuple M = ( K, Σ , Γ , Δ , s, F ) where • K is a finite, nonempty set of states, • Σ is an input alphabet, • Γ is a stack alphabet, • s ∈ K is the initial state, • F ⊆ K is a set of final state, • Δ is a transition relation, a finite subset of ( K × (Σ ∪{ e } ) × Γ ∗ ) × ( K × Γ ∗ ). Note that Δ is a relation, not a function, thus PAs are non- deterministic. Unlike FAs, deterministic pushdown automata are not equivalent in power with nondeterministic pushdown automata. Specifically, nondeterministic PA can recognize cer-automata....
View Full Document

This note was uploaded on 09/22/2011 for the course COMP 272 taught by Professor Prof.tai during the Spring '10 term at HKUST.

Page1 / 8

11 - 11: Pushdown Automata Every regular language is a CFL....

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online