CSC 320 Midterm: CSC 320 UVic Midterm90

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1. (a) state the pumping lemma for regular languages. (b) let w = a k b a k 2 w = xyz , and y . Describe all possible ways of choosing x , y , z such that (c) apply the pumping lemma to w = a k b a k 2 to prove that. How does this simplify the argument you gave for (c): use the algorithm described in class (or in the text) to create a dfa equivalent to s 3. String the fa with start state s 1 and transitions: iiiiiiiiiiiiiiiiiiiiiiiiii. Next state iiiiiiiiiiiiiiiiiiiiiiiiii s 1 iiiiiiiiiiiiiiiiiiiiiiiiii s 1 iiiiiiiiiiiiiiiiiiiiiiiiii s 2 iiiiiiiiiiiiiiiiiiiiiiiiii s 3 iiiiiiiiiiiiiiiiiiiiiiiiii s 3 iiiiiiiiiiiiiiiiiiiiiiiiii s 4 iiiiiiiiiiiiiiiiiiiiiiiiii a a s 2 s 4 s 1 s 2 bb s 3. The set of nal states includes only s 2. 3. (a) give a context-free grammar for l 1.

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