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355hw1sols09

# 355hw1sols09 - HW1 Solution 1.4 a L1 = cfw_w | w has at...

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HW1 Solution 1.4 a. 1 { | has at least three 's} L w w a = a a a b b b a,b 2 { | has at least two 's} L w w b = b b a a a,b Combining them using the intersection construction gives the DFA: a a a a a a a a a b b b b b b b b a a a,b b b b c. 1 { | has an even number of 's} L w w a = a a b b

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2 { | has one or two 's} L w w b = b b b a a a a,b Combining them using the intersection construction gives the DFA: b b b b b b b a a a a a a a a b e. 1 { | starts with an } L w w a = a a,b b a,b 2 { | has at most one } L w w b = b b a a a,b
Combining them using the intersection construction gives the DFA: a a,b b b a a a,b a b b f. 1 { | has an odd number of ' } L w w a s = b b a a 2 { | ends with a } L w w b = a b a b

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Combining them using the intersection construction gives the DFA: a a b b b b a a g. 1 { | has even length} L w w = a,b a,b 2 { | has an odd number of 's} L w w a = b b a a
Combining them using the intersection construction gives the DFA: b b b a a a a b 1.6 c. 0 1 0 1 1 0,1 0 0 1 e. 0 1 0,1 0,1 0,1 0,1

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l.
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• Summer '05
• Joel
• Formal language, Regular expression, Regular language, Nondeterministic finite state machine, intersection construction

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355hw1sols09 - HW1 Solution 1.4 a L1 = cfw_w | w has at...

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