Automata on flows Petter Remen Abstract: We introduce a coalgebraic generalization of an infinite word, namely a sourced flow, followed by a definition of what it means for an automaton to accept a sourced flow, thereby generalizing the notion of \omega-regularity. We show that this definition yields a finitary description of acceptance for finite sourced flows. We end by presenting three characterization results on regular classes of finite sourced flows.