The state complexity of L^2 and L^k
<|reference_start|>The state complexity of L^2 and L^k: 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.<|reference_end|>
@article{rampersad2004the,
    title={The state complexity of L^2 and L^k},
    author={Narad Rampersad},
    journal={arXiv preprint arXiv:cs/0410032},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0410032},
    primaryClass={cs.CC cs.FL}
}