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Announcements Formal definition of PDAs Turn in your H/W #5 Pick up a copy of H/W #6 Atri Rudra May 12 A. Rudra, CSE322 A request Puzzle for the day If you do not understand something in class, ASK a question Even if it is a doubt in the slides Where I am thinking of going a bit fast A. Rudra, CSE322 3 Last Lecture Design a PDA for the following language { xy | x,y∈ {0,1}* and |x|=|y| but x≠ y } A. Rudra, CSE322 PDA = DFA + stack 4 1101 # 1011 How does 1101 look when it is pushed onto a stack ? It looks the same as the stuff after the # Just “match” off the rest Let’s recap by another example { w # wR | w∈ {0,1}* } A. Rudra, CSE322 Let’s look at a string in the language Designed a few Push Down Automatons 2 5 A. Rudra, CSE322 1 0 1 1 6 1 Questions ? { w # wR | w∈ {0,1}* } ε,ε → $ A B 0,ε → 0 1,ε → 1 C 1,1 → ε 0,0 → ε #,ε → ε D ε,$ →ε A. Rudra, CSE322 7 Formal definition of a PDA ε,ε → $ Symbols that can be pushed and popped δ : Q×Σ U{ε}×Γ U {ε}→ 2Q× Γ U {ε} Transition function s∈ Q : start state F⊆ Q : final states A. Rudra, CSE322 Use non-determinism more critically { wwR | w∈ {0,1}* } A. Rudra, CSE322 A B Q = {A,B,C,D} Σ= {0,1,#} #,ε → ε Γ= {0,1,$,#} D C ε,$ →ε s=A F={D} The transition from C to D 9 Up next… 8 Using the previous example PDA M = Q,Σ,Γ,δ,s,F Q : set of states Σ : input alphabet Γ : stack alphabet A. Rudra, CSE322 0,ε → 0 1,ε → 1 1,1 → ε 0,0 → ε (D,ε) ∈ δ(C,ε,$) A. Rudra, CSE322 10 In other words… 11 A. Rudra, CSE322 12 2