State Complexity of Insertion

초록

It is well known that the resulting language obtained by inserting a, regular language to a regular language is regular. We study the nondeterministic and deterministic state complexity of the insertion operation. Given two incomplete DEAs of sizes m, and n we give an upper bound ern (m + 2) . 2(mn-m-)1 . 3(m) and find a lower bound for an asymptotically tight bound. We also present the tight nondeterministic state complexity by a fooling set technique. The detertninistic state Complexity of insertion is 2(Theta(mn))and the nondeterministic state complexity of insertion is precisely mn + 2m, where rn, and n are the size of input finite automata. We also consider the state complexity of insertion in the case where the inserted language is bifix-free or non-returning.

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