Abstract
We study Kuratowski algebras generated by prefix-free languages under the operations of star and complement. Our results are as follows. Five of 12 possible algebras cannot be generated by any prefix-free language. Two algebras are generated only by trivial prefix-free languages, the empty set and the language \(\{\varepsilon \}\). Each of the remaining five algebras can be generated, for every \(n\ge 4\), by a regular prefix-free language of state complexity n, which meets the upper bounds on the state complexities of all the languages in the resulting algebra.
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