Monoids and the State Complexity of the Operation root(<i>L</i>)

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 generated by two elements. Also, we give good bounds on the worst-case state complexity of root(L). In turn, these new results concerning root(L) allow us to improve previous bounds given for the state complexity of two-way deterministic finite automata

On Deterministic Finite Automata and Syntactic Monoid Size, Continued

We continue our investigation on the relationship between regular languages and syntactic monoid size. In this paper we con rm the conjecture on two generator transformation semigroups. We show that for every prime n 7 there exist natural numbers k and ` with n = k + ` such that the semigroup Uk;` is maximal w.r.t. its size among all (transformation) semigroups which can be generated with two generators