304_HW2_F11

# 304_HW2_F11 - a b c Construct non deterministic finite...

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UML CS Foundations 91.304 (section 201) Fall, 2011 1 of 2 Homework Set #2 Assigned: Friday, 9/9 Due: Wednesday, 9/21 (start of lecture) This assignment covers textbook material in Chapter 1, Sections 1.1-1.2. Note: Refer to course web site for homework policies. Remember to attach signed honor statement. 1. (10 points) DFA’s : Generalize Example 1.13 (p. 39) for a 5-symbol input alphabet: { <RESET>, 0, 1, 2, 3 } so that it accepts strings for which the sum of the associated numbers is a multiple of 3. 2. (15 points) DFA’s : Assume that the alphabet is { a, b }. Construct a deterministic finite automaton recognizing the following language (describe the automaton using its 5-tuple and pictorial diagram): { w | w consists of an odd number of a ’s followed by a string consisting of 1 or more b ’s.} 3. (15 points) DFA’s : For the state diagram below describe the language that it recognizes: 4. (30 points) NFA’s : In both cases below assume that the alphabet is {

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Unformatted text preview: a, b, c }. Construct non deterministic finite automata recognizing each of the following languages (describe each automaton using its 5-tuple and pictorial diagram): a) { w | w contains the substring ab and the substring cb } b) { w | w contains the substring ab and the substring bc , where the two substrings may overlap, but bc cannot come before ab } 5. (15 points) NFA-to-DFA Conversion: Convert the NFA below to an equivalent DFA using the process given in the proof of Theorem 1.39 (p. 55-56). Show both the 5-tuple and pictorial diagram for your DFA. After describing the result, remove any unreachable states to further simplify your DFA. q 1 q 2 q 3 a a b a b b q 1 q 3 ε a b q 2 UML CS Foundations 91.304 (section 201) Fall, 2011 2 of 2 6. (15 points) Closure of Regular Languages : Prove that if L 1 and L 2 and L 3 are regular languages, then the following language L 4 is also regular: ) ( 3 2 1 4 L L L L ∩ ∪ =...
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304_HW2_F11 - a b c Construct non deterministic finite...

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