Explain finite automata with epsilon transition

An informal treatment of €-NFA’s, using transition diagrams with f allowed as a label. In the examples to follow, think of the automaton as accepting those sequences of labels along paths from the start state to an accepting state. However, each e along a path is “invisible” j i.e., it contributes nothing to the string along the path.

In Fig. is an €-NFAthat a.ccepts decimal numbers consisting of:2. A string of digits,
1. An optional + or – sign,
3. A decimal point, and
4. Another string of digits. Either this string of digits, or the string (2) can be empty, but at least one of the two strings of digits must be nonempty.

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