The state complexity of L2 and Lk

Authors:
Narad Rampersad
Affiliations:
School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada
Venue:
Information Processing Letters
Year:
2006

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Abstract

We show that if M is a DFA with n states over an alphabet with at least two letters and L = L(M), then the worst-case state complexity of L2 is n2n - 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.