Let L be any language. Let us define the transpose of L to be the language of
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Let L be any language. Let us define the transpose of L to be the language of exactly those words that are the words in L spelled backward. If w El, then reverse(w) El. For example, if
L = {a abb bbaab bbbaa}
then
transpose(L) = {a bba baabb aabbb}
(i) Prove that if there is an FA that accepts L, then there is a TG that accepts the transpose of L.
(ii) Prove that if there is a TG that accepts L, then there is a TG that accepts the transpose of L.
(iii) Prove that transpose(L1L2) = transpose(L2)· transpose(L1).
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i Suppose that there is an FA A that accepts L This means the set of states of A has the form q0 q1 qn and there is a transition function tA taking each state to a set of states a run on A is given by ...View the full answer
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