The state complexity of L^2 and L^k

Details The state complexity of L^2 and L^k The state complexity of L^2 and L^k

2004-10-14

arxiv.org/abs/cs/0410032v2

Computer Science

Computational Complexity

5 pages, 1 figure; some errors corrected

Scientific paper

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 L^2 is n*2^n - 2^{n-1}. If,
however, M is a DFA over a unary alphabet, then the worst-case state complexity
of L^k is kn-k+1 for all k >= 2.

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