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# hw_03 - Problem Set 3 Fall 09 Due Thursday Oct 22 at 11:00...

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Unformatted text preview: Problem Set 3 Fall 09 Due: Thursday Oct 22 at 11:00 AM in class (i.e., Room 103 Talbot Lab) Please follow the homework format guidelines posted on the class web page: http://www.cs.uiuc.edu/class/fa09/cs373/ 1. CFG construction. [ Points : 30] Construct CFGs for the following languages. Give a brief explanation of how your grammar works and what each nonterminal stands for. A = { a i b j | i 6 = j } B = { a i b j c k | i ≤ j or j ≤ k } C = { x ∈ { , 1 } * | x is not of the form ww } D = { x ∈ { a,b } * | x contains twice as many a 's than b 's } E = { x ∈ { a,b } * | x is not a palindrome and | x | is even } F = { a i b j | 2 i + 3 ≤ j ≤ 4 i + 5 } 2. CFG interpretation. [ Points : 15] What is the language of the following CFG? Justify your answer. S → A 1 B A → A | B → B | 1 B | 3. Proof. [ Points : 30] Consider the context-free grammar: S → S 1 S | 1 S S | Describe L ( G ) in English, and prove that your answer is correct, i.e. G generates all strings you've described and only those strings.described and only those strings....
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hw_03 - Problem Set 3 Fall 09 Due Thursday Oct 22 at 11:00...

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