flac-hw6 - ” strings with more than one “ ” are...

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FLAC Assignment 6 Exercise 1. Give context-free grammars that generate the following languages. In all parts the alphabet is Σ is { 0 , 1 } . a. { w | w contains at least three 1 s } b. { w | w starts and ends with the same symbol } c. { w | the length of w is odd } d. { w | the length of w is odd and its middle symbol is a 0 } e. { w | w = w R , i.e., w is a palindrome (of either odd or even length) } f. The empty set (Note: You may check your answers to parts (a) and (d) in the book; see Exercise 2.4 on page 128 and 132. But don’t peek without first trying it yourself!) Exercise 2. Give the state diagrams of pushdata automata for the following languages. d. The language of Exercise 1(d). e. The language of Exercise 1(e). f. { w # v | w has more occurrences of 1 than does v } . You may assume that the input string has no more than one occurrence of “
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Unformatted text preview: # ”; strings with more than one “ # ” are don’t-care inputs that can be ignored to simplify the design of your PDA. Exercise 3. Show the intersection of a context-free language C with a regular language R is always context-free. Exercise 4. Show that the language { n 1 m n 1 m | n ≥ } is not context-free. Exercise 5. Show that the language { ww | w ∈ ( + 1 ) * } is not context-free. Hint: Intersect with * 1 * * 1 * and use the results from Exercises 3 and 4. Exercise 6 (bonus). Is the following language context-free? Prove your answer. { ww | w ∈ ( a + b ) * , w ∈ ( a + b ) * , w 6 = w , and | w | = | w |} Page 1...
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