Kuratowski Algebras Generated by Prefix-, Suffix-, Factor-, and Subword-Free Languages Under Star and Complementation

摘要

We study Kuratowski algebras generated by prefix-, suffix-, factor-, and subword-free languages under the operations of star and complementation. We examine 12 possible algebras, and for each of them, we decide whether or not it can be generated by a prefix-, suffix-, factor-, or subword-free language. In each case when an algebra can be generated by such a language, we show that this language can be taken to be regular, and we compute upper bounds on the state complexities of all the generated languages. Finally, we find generators that maximize these complexities.