The state complexity of L^2 and L^k
Computational Complexity
2009-03-29 v2 Formal Languages and Automata Theory
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 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.
Cite
@article{arxiv.cs/0410032,
title = {The state complexity of L^2 and L^k},
author = {Narad Rampersad},
journal= {arXiv preprint arXiv:cs/0410032},
year = {2009}
}
Comments
5 pages, 1 figure; some errors corrected