Unformatted text preview: (copied below) 2.3 a. Define a language L smallerthanw If w = aabbc, under your definition, what is L smallerthanw ? b. For strings r,s,v,w with r < s and v < w, prove or disprove (i) rv < sw (ii) v R < w R ( iii) w R < v R 2.4. Suppose Σ = {a,b,c} and v = v 1 ,..., v n , n = 3, v = abbc. Give all possible divisions of v into three substrings, v = v 1 v 2 v 3 . 2.5. Let Σ = {a,b,c} with languages L ε = {ε}, L ∅ = , ∅ L 3k = { w so that w = 3k for some k >= 0 }, L a = { w  w contains an a} Find: a. L ∅ L 3k b. L ε L 3k f Suffix (L a ) 5. a. If w = aac and x = cb, list all the strings in Shuffle(w,x) and in Shuffle(x,w) b. If L 1 = {a, aa, aab, abc, cba} and L 2 = {a, ba}, list the strings in L 1 / L 2 c. If L 1 = {strings over a,b,c with even number of a’s} and L 2 = {strings with at least one a over a,b,c}, describe the strings in L 1 / L 2...
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 Spring '11
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