hw1_sol - Formal Languages and Theory of Computation...

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Unformatted text preview: Formal Languages and Theory of Computation Homework 1 Solutions 2009.10.20 1.3. Here is the state diagram. 1.6. a. The formal description of the DFA is M = ( { q 1 ,q 2 ,q 3 ,q 4 } , { , 1 } ,δ,q 1 , { q 4 } ), where δ is given by following table. 1 q 1 q 2 q 3 q 2 q 2 q 2 q 3 q 4 q 3 q 4 q 4 q 3 Then, we show that L ( M ) = { w | w begins with a 1 and ends with a 0 } . First, ob- serve that any string which begins with a 0 will leave M in state q 2 , so it is rejected. On the other hand, any string which begins with a 1 and ends with a 1 will leave M in state q 3 , while any string which begins with a 1 and ends with a 0 will leave M in state q 4 . Since the set of accept states is { q 4 } , we complete the proof. i. The DFA is M = ( Q, Σ ,δ,q ,F ), where 1. Q = { q ,q 1 ,q 2 ,q 3 } , 2. Σ = { , 1 } , 3. δ is 1 q { q 3 } { q 1 } q 1 { q 2 } { q 2 } q 2 { q 3 } { q 1 } q 3 { q 3 } { q 3 } 4. q is the start state, and 5. F = { q 1 ,q 2 } (p.s. Show that L ( M ) = { w | every odd position of w is a 1 } .) 1 k. The DFA is ( Q,...
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This note was uploaded on 11/25/2009 for the course FORMAL formal taught by Professor Pro during the Spring '09 term at National Cheng Kung University.

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hw1_sol - Formal Languages and Theory of Computation...

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