pushdown automata (pda)

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Transition FunctionDepending on the current state, the stack symbol ontop, and optionally the input symbol, a <strong>pda</strong> makes astate transition and pushes a string of stack symbolsback to the stack.Let’s note a few things about δ,δ : Q × (Σ ∪ {λ}) × Γ → 2 Q×Γ∗ .The value is a finite subset of Q × Γ ∗ .A move is possible without using an input symbol.No move is possible with an empty stack.The reading of input never goes “backwards”.Pushdown Automata – p. 4
Examples of δSuppose δ(q 1 ,a,b) = {(q 2 ,cd), (q 3 ,λ)} for n<strong>pda</strong> M.When M is in state q 1 , the input symbol is a and the topof stack is b, one of two things can happen:M transits to state q 2 and replace b by cd (c on topof d).M transits to state q 2 and remove b.A transition function can be represented by a graph,where an edge from q i to q j labeled by a,b,y means(q j ,y) ∈ δ(q i ,a,b).Pushdown Automata – p. 5
Page 1 and 2: Pushdown AutomataNotes on Automata
Page 3: Pushdown AutomataA nondeterministic
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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