hw1-2007-sol

# hw1-2007-sol - Homework 1, Solution Q1 [10 pts] P.54,...

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Homework 1, Solution ε Q1 [10 pts] P.54, Ex.2.2.4: b), c) b) c) Q2 [10 pts] P.54 Ex.2.2.5: c 0 1 0 1 0,1 1 0 1 1 0 0 Q3 [20 pts] P.54 Ex.2.2.8 a) [10 pts] Proof Basis: q a q = ) , ( δ for all states of A and a particular input symbol a . Induction: since a a a n n = 1 and q a q = ) , ( , we have q a q a q a q a a q a q n n n = = = = = = ) , ( ) , ( ˆ ... ) , ( ˆ ) ), , ( ( ˆ ) , ( ˆ 1 1 b) [10 pts] Let 0 q be the start state of this DFA. We will discuss the following two conditions. If ) ( 0 A L q , it means 0 q is an accepting state. According to a), 0 0 ) , ( ˆ q a q n = , that is, all input with the format n a will be accepted. So ) ( } { * A L a . If ) ( 0 A L q , it means 0 q is not an accepting state. According to a), 0 0 ) , ( ˆ q a q n = , that is, all input with the format n a will not be accepted. So Φ = ) ( } { * A L a .

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Since 0 q either belongs to L(A) or not, we get the conclusion that either ) ( } { * A L a or Φ = ) ( } { * A L a . Q4 [15 pts + 5 bonus pts] Design an NFA for each of the languages in P.54 Ex.2.2.5.
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## This note was uploaded on 03/31/2008 for the course CS 150 taught by Professor Jiang during the Spring '07 term at UC Riverside.

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hw1-2007-sol - Homework 1, Solution Q1 [10 pts] P.54,...

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