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Unformatted text preview: CS 341 Automata Theory Elaine Rich Homework 14 Due Friday, Dec.8 at 11:59 pm 1) Construct unrestricted grammars that generate each of the following languages L : a) { ww R w : w { a , b }*}. b) { a n b m c n + m : n , m > 0}. c) { a n b m c nm : n , m > 0}. 2) Construct an unrestricted grammar to compute the following function: f : {a, b} + { a , b }* f ( s ) = if  s  is even then s if  s  is odd then s with the middle character chopped out (Hint: The answer to this one is fairly long, but it's not very complex. Think about how you would use a Turing Machine to solve this problem.) CS 341 Automata Theory Elaine Rich Homework 14 Answers 1) Construct unrestricted grammars that generate each of the following languages: a) L = { ww R w : w { a , b }*} S S S 1 # S 1 a S 1 a First generate wTw R # S 1 b S 1 b S 1 T Take each character of w R , starting at the left. Make a copy of it and slide it to the right of the # to create the second w. Use 1 for a and 2 for b. Ta T 1 A Well move A for a, B for b. And well transform each character Tb T 2 B of w R as it is considered: a will be 1, b will be 2. These two rules will handle the first such character. 1 a 1 1 A These next four will do this for characters 2 through n of w R . 1 b 1 2 B 2 a 2 1 A 2 b 2 2 B A a a A Push As and Bs to the right until they hit #. A b b A B b b B B a a B A # # a Jump across # B # # b 1 # # a Once all of w R has been converted to 1s and 2s (i.e., its all 2 # # b been copied), push # leftward converting 1s back to as and 2s to bs....
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This note was uploaded on 12/03/2009 for the course CS 341 taught by Professor Rich during the Fall '08 term at University of Texas at Austin.
 Fall '08
 Rich

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