Sedlitz, G. (2017). Abzählung von Automaten, formalen Sprachen und verwandten Strukturen [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2017.37840
One way of characterizing regular languages is through finite deterministic or nondeterministic automata. A counting sequence can be obtained by considering automata with n states over an input alphabet of size k. We study the asymptotic behaviour of this sequence for different classes of automata and their relations to other structures. Upper and lower bounds are obtained for the number of automata and the number of accepted languages using a variety of methods ranging from number theory and graph theory to complex analysis. Furthermore, we will introduce a method of random smpling for initially connected automata.