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Sketch of a deterministic finite automaton (DFA) for the following regular language (type 3):$$L ~=~ \{ w \in \{0,1\}^* ~:~ \text{ for every 0 there must be a 1 somewhere behind (multiple 0s may share the same 1)} \} $$
This is an infinite language, with, for example, the following words:$$ L ~=~ \{ \varepsilon, 1, 01, 101, 10001, ~... \} $$