pushdown automata (pda)

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IntroductionRegular languages correspond to the class of dfa’s. Isthere a class of automata for context-free languages?The class of automata for context-free languagesshould be able to, among other things, count withoutlimit (for language such as {a n b n : n ≥ 0}) and storeand match a sequence of symbols in the reverse order(for {ww R : w ∈ Σ ∗ }). This suggests using stack asstorage.The class of automata using stack as storage is calledthe pushdown automata (pda).Pushdown Automata – p. 2
Pushdown AutomataA nondeterministic pushdown automaton (npda) isdefined by a septuple (7-tuple)M = (Q, Σ, Γ,δ,q 0 ,z,F),Q is a finite set of statesΣ is a finite set called input alphabetΓ is a finite set called stack alphabetδ : Q × (Σ ∪ {λ}) × Γ → 2 Q×Γ∗ is the transitionfunctionq 0 ∈ Q is the initial statez ∈ Γ is the stack start symbolF ⊆ Q is the set of final statesPushdown Automata – p. 3
Page 1: Pushdown AutomataNotes on Automata
Page 5 and 6: Examples of δSuppose δ(q 1 ,a,b)
Page 7 and 8: Language Accepted by An npdaLet M =
Page 9 and 10: Another ExampleConsider the set L =
Page 12: Proof L(G) ⊆ L(M)Consider partial
Page 15 and 16: Basic IdeaHere we want the sententi
Page 17 and 18: ProofWe show that for all q i ,q j
Page 19 and 20: Deterministic cfgA language L is sa
Page 21 and 22: Grammars for Compiler DesignThe dec
Page 23 and 24: Pumping LemmaLet L be an infinite c
Page 25 and 26: Closure PropertiesThe set of contex
Page 27 and 28: Regular IntersectionLet L 1 be cont

pushdown automata (pda)

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