pushdown automata (pda)

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ProofSuppose that L 1 ,L 2 are context-free languages.U = L 1 ∪ L 2 , C = L 1 · L 2 , and S = L ∗ 1 . The variable setsare disjoint.The grammar for U is to add a new start variable S Uand a rule S U → S 1 |S 2 .The grammar for C is to add a new start variable S Cand a rule S C → S 1 S 2 .The grammar for S is to add a new start variable S Uand a rule S S → S 1 S S |λ.Counter-examples can be given to prove thenon-closedness of intersection and complementation.Pushdown Automata – p. 26
Regular IntersectionLet L 1 be context-free and L 2 be regular. Then L 1 ∩ L 2is context-free.To prove, we construct an n<strong>pda</strong> given the n<strong>pda</strong> M 1 forL 1 and dfa M 2 for L 2 , which simulates simultaneousexecution of M 1 and M 2 .Pushdown Automata – p. 27
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 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: Closure PropertiesThe set of contex

pushdown automata (pda)

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