pushdown automata (pda)

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Instantaneous DescriptionThe relevant information at any instant is the currentstate, q, the unread part of input string, w, and thecontent of stack, u. The triplet (q,w,u) is called aninstantaneous description (ID) of an npda.A move (or step) from an ID to another is denoted bythe symbol ⊢,(q,aw,bx) ⊢ (p,w,yx) ⇔ (p,y) ∈ δ(q,a,b).A sequence of moves is denoted by ∗ ⊢, e.g.,(q 1 ,w 1 ,x 1 ) ∗ ⊢ (q 2 ,w 2 ,x 2 ).Pushdown Automata – p. 6
Language Accepted by An npdaLet M = (Q, Σ, Γ,δ,q 0 ,z,F) be an npda. The languageaccepted by M is the set of stringsL(M) = {w ∈ Σ ∗ : (q 0 ,w,z) ∗ ⊢ (p,λ,u),p ∈ F,u ∈ Γ ∗ }L(M) is the set of input strings that can make M ina final state at the end of the input string.The final stack content is irrelevant.It turns out the set of languages acceptable by npda isequal to the set of context-free languages.Pushdown Automata – p. 7
Page 1 and 2: Pushdown AutomataNotes on Automata
Page 3 and 4: Pushdown AutomataA nondeterministic
Page 5: Examples of δSuppose δ(q 1 ,a,b)
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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