State Complexity of Basic Operations on Non-returning Regular Languages

We consider the state complexity of basic operations on non-returning regular languages. For a non-returning minimal DFA, the start state does not have any in-transitions. We establish the precise state complexity of four Boolean operations (union, intersection, difference, symmetric difference), catenation, reversal, and Kleene-star for non-returning regular languages. Our results are usually smaller than the state complexities for general regular languages and larger than the state complexities for suffix-free regular languages.

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