NFA with epsilon transitions for a or b

This epsilon-NFA accepts the language described by the regular expression a|b. It begins at q0 and takes one of two epsilon transitions, which change state without consuming an input symbol. The upper branch reaches q1 and accepts an a; the lower branch reaches q2 and accepts a b. Both branches end at qf, the accepting state. The drawing is a small version of the union rule used in Thompson construction: introduce a new start state, split by epsilon to the alternatives, then join successful alternatives at a shared final state. Because epsilon moves consume nothing, the choice of branch is made before the machine reads the only input symbol.