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Unformatted text preview: COT 5310 Assignment 7 Key, Fall 2007 1. Present the description of a PDA (in words) that accepts L A (see page 253 of Notes). You may assume that [ i ] is a single symbol. A PCP instance over Σ consists of two vectors x, y over Σ ∗ where  x  =  y  = n . Let I = { 1 , . . . , n } and be disjoint from Σ (we use just i instead of [ i ] to denote the index). L A is the language generated by the grammar A → x i A i  x i i for i ∈ I over the alphabet Σ ′ = Σ ∪ I . So L A = braceleftbig x i 1 x i 2 . . . x i k 1 x i k i k i k − 1 . . . i 2 i 1 : 1 ≤ i j ≤ n for 1 ≤ j ≤ k and i j ∈ I and x i j ∈ Σ ∗ bracerightbig . To make a PDA that accepts this language, use Σ ′ = Σ ∪ I as the stack symbols, with Z as the bottom of stack marker. We’ll push symbols until we reach an element i ∈ I . Then we’ll pop ( x i ) R from the top of the stack and repeat. If we run out of input and have an empty stack, then we’re in L A . 1) Read in elements of Σ and push them onto the stack. When encountering some i ∈ I , push it onto the stack and move to step 2). 2) Pop i from the stack and check if w i R is on top of the stack. If it isn’t, we’re not in L A so transition to a nonaccepting state r ). If w i R is on top, and the bottom of stack symbol is exposed, transition to an accepting state a )....
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 Spring '08
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 Universal quantification, λ, HIJK

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