State complexity of deletion and bipolar deletion

초록

It is well known that the language obtained by deleting an arbitrary language from a regular language is regular. We give an upper bound for the state complexity of deleting an arbitrary language from a regular language and a matching lower bound. We show that the state complexity of deletion is [respectively, ] when using complete (respectively, incomplete) deterministic finite automata. We show that the state complexity of bipolar deletion has an upper bound [respectively ] when using complete (respectively, incomplete) deterministic finite automata. In both cases we give almost matching lower bounds.

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