Epsilon-NFA

An epsilon-NFA is a nondeterministic finite automaton that may traverse transitions labelled $ϵ$ without consuming an input symbol.

An automaton transition that consumes no input symbol. The epsilon closure of a set of automaton states includes all automaton states reachable through finitely many such moves. Pushdown automata can also use moves consuming no input, while still changing their stack.

The epsilon closure of a state set $S$ consists of every state reachable from $S$ using zero or more epsilon transitions.

The subset construction converts an epsilon-NFA into a deterministic finite automaton. Its states are subsets of NFA states, its initial state is the epsilon closure of the NFA initial state, and every symbol transition is followed by another epsilon closure.