Question: please solve it complete in 30 minute (b) Leth: {0,1} + {a,b) be the function defined by h(e) = e, h(0) = aa and h(1)

please solve it complete in 30 minute

please solve it complete in 30 minute (b) Leth: {0,1} + {a,b)

(b) Leth: {0,1} + {a,b) be the function defined by h(e) = e, h(0) = aa and h(1) = b, and for words of length two or greater: h(a,a2...an) = n(a)h(az)...hlan) for n > 2 and a; (0,1}. For a language L C {0,1}' we define h(L) = {h(w)|WE L} S {a,b)* For cach of the following languages, give a regular expression over {a,b} that Corresponds to h(L): (i) L = {0mi"|m, n >0}. (3] (ii) L = {w {0,1} | w contains 010 as a subword). [3] (c) Is it possible to write regular expressions representing the following languages over the alphabet {a,b)? If yes, write the regular expression, or else prove that it is impossible. (i) {www {a,b)"}. Here wR stands for the reverse of the word w. (4) (ii) {a" -1 n = 1,2,...}. = (4)

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