The state complexity of L2 and Lk
Narad Rampersad
Abstract
We show that if M is a DFA with n states over an arbitrary alphabet and L = L(M), then the worst-case state complexity of L2 is n*2n - 2n-1. If, however, M is a DFA over a unary alphabet, then the worst-case state complexity of Lk is kn-k+1 for all k >= 2.
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