9.14.08 - delta3 is constructed from delta3[x1,x2,a...

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Sheet1 Page 1 The construction of a DFA, M3, such that L(M3) = L(M1) intersect L(M2) is given by: Let M1 = (Q1, sigma, delta1, q1, F1) Let M2 = (Q2, sigma, delta2, q2, F2) Let S1 x S2 mean the cross product of sets S1 and S2, all ordered pairs, Then M3 = (Q1 x Q2, sigma, delta3, [q1,q2], F1 x F2) where [q1,q2] is an ordered pair from Q1 x Q2,
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Unformatted text preview: delta3 is constructed from delta3([x1,x2],a) = [delta1(x1,a), delta2(x2,a)] for all a in sigma and all [x1,x2] in Q1 x Q2. We choose to say the same alphabet is used in both machines, but this works in general by picking the alphabet of M3 to be the intersection of the alphabets of M1 and m2 and using all 'a' from this set....
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