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

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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....
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## 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.

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

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