The index of a language is the number of Myhill-Nerode classes that it has. It is also equal to the number of states in the minimal DFA for the language. What is an example of a language that has a different index from its reversal?
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The $k$th letter equals $a$, for fixed $k$, assuming a two letter alphabet.
This generic answer is made precise in the comment by @AntonTrunov below.
Hendrik Jan
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