Monoids and the State Complexity of the Operation root(L)
Bryan Krawetz · 2004
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii In this thesis, we cover the general topic of state complexity. In particular, we examine the bounds on the state complexity of some different representations of regular languages. As well, we consider the state complexity of the operation root(L). We give quick treatment of the deterministic state complexity bounds for nondeterministic finite automata and regular expressions. This includes an improvement on the worst-case lower bound for a regular expression, relative to its alphabetic length. The focus of this thesis is the study of the increase in state complexity of a regular language L under the operation root(L). This operation requires us to examine the connections between abstract algebra and formal languages. We present results, some original to this thesis, concerning the size of the largest monoid