T F L T C A S Turku Centre for Computer Science University of Turku Lemminkäisenkatu 14, 20520 Turku, Finland asalomaa@it.utu.fi E F L Michael Domaratzki Jodrey School of Computer Science Acadia University Wolfville, NS B4P 2R6 Canada mike.domaratzki@acadiau.ca Abstract We survey recent results on the enumeration of formal languages. In particular, we consider enumeration of regular languages accepted by de- terministic and nondeterministic finite automata with n states, regular lan- guages generated by regular expressions of a fixed length, and ω-regular languages accepted by Müller automata. We also survey the uncomputabil- ity of enumeration of context-free languages and more general structures. 1 Introduction Given a set of objects, enumeration asks “how many distinct objects are there?” Easy examples of enumeration problems are “how many binary sequences of 1