pushdown automata (pda)

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{a n b n : n ≥ 0} ∪ {a n b 2n : n ≥ 0}This language is a cfl but not dcfl.It is a cfl since L = L 1 ∪ L 2 and both L 1 = {a n b n : n ≥ 0}and L 2 = {a n b 2n : n ≥ 0} are cfls.Consider ̂L = L ∪ {a n b n c n : n ≥ 0}. It can be shown bypumping lemma for cfg that ̂L cannot be a cfl.Suppose L is dcfl. Then we can construct an npda ̂Mfor ̂L from a dpda M for L, as depicted in Figure 7.4.That’s a contradiction.Pushdown Automata – p. 20
Grammars for Compiler DesignThe decision whether a string is in the language of adpda can be made quickly as there is no backtrackinginvolved.In order to decide if a string is in a context-freegrammar, if there were some way to pinpoint the nextrule to use in the derivation, then the parsing processwould also be very fast.The material introduced here is important for the studyof compilers, but not directly related to later subjects inthis course.Pushdown Automata – p. 21
Page 1 and 2: Pushdown AutomataNotes on Automata
Page 3 and 4: Pushdown AutomataA nondeterministic
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: Deterministic cfgA language L is sa
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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