hw3-1 - CSE105: Automata and Computability Theory Winter...

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Unformatted text preview: CSE105: Automata and Computability Theory Winter 2011 Homework #3 Due: Tuesday, February 1st, 2011 Problem 1 Pumping Lemma practice. For each of the following languages, and for a pump- ing length p , give a string w that can be used to establish that the language is not regular. For example, in class we used the string w = 0 p 1 p for the language L = w { , 1 } * w has as many s as 1 s . a. L a = n 1 n over = { , 1 } . b. L b = a 1 b 2 c a + b > c over = { , 1 , 2 } . c. L c = xx R over = { a , b ,..., z } . Here x R denotes the symbol-by-symbol reverse of x . In other words, if x = x 1 x 2 ...x n then x R = x n x n- 1 ...x 1 . d. L d = 1 r r is prime over = { 1 } . e. L e = m 1 n m is a multiple of n over = { , 1 } . (Note that 0 is a multiple of every number.) Problem 2 Let REGEXP be the language of valid regular expressions over { a , b } . That is, REGEXP is the set of all strings over the symbols = a , b , ( , ) , , * , , that are valid regular expressions. For example, the string valid regular expressions....
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This note was uploaded on 08/31/2011 for the course CSE 105 taught by Professor Paturi during the Spring '99 term at UCSD.

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hw3-1 - CSE105: Automata and Computability Theory Winter...

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