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Show that if a language L C {a,b}* is recognised by some finite au- tomaton, then so are the following languages, consisting of all the

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Show that if a language L C {a,b}* is recognised by some finite au- tomaton, then so are the following languages, consisting of all the prefixes and suffixes of the words in L: (i) Pref(L) = {x {a,b}* | xy EL for some y E {a, b}*}, (ii) Suff(L) = {y {a,b}* | xy EL for some x E {a,b}*}

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