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Unformatted text preview: R R L x x = where R x stands for x reversed. 4. 4.2.1 Suppose h is the homomorphism from the alphabet {0,1,2} to the alphabet {a,b} defined by: h(0)=a, h(1)=ab, and h(2)=ba. a) What is h(0120)? b) What is h(21120)? c) If L is the language L(01*2), what is h(L)? d) If L is the language L(0+12), what is h(L)? e) Suppose L is the language {ababa}, that is, the language consisting of only the one string ababa. What is h1 (L)? f) If L is the language L(a(ba)*), what is h1 (L)? 5. 4.2.7 by machine construction. If 1 2 n w a a a = L and 1 2 n x bb b = L are strings of the same length, define alt(w,x) to be the string in which the symbols of w and x alternate, starting with w , that is, 1 1 2 2 n n a b a b a b L . If L and M are languages, define alt(L,M) to be the set of strings of the form alt(w,x), where w is any string in L and x is any string in M of the same length. Prove that if L and M are regular, so is alt(L,M)....
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 Fall '07
 HOPCROFT

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