 to handle epsilon transitions. Let’s define <span class="math inline">\(\text{epsilon-paths}(q)\)</span> as the set of all paths from state <span class="math inline">\(q\)</span> to any other state using only epsilon transitions:</p>
<p><span class="math display">\[
\text{epsilon-paths}(q) = \{\langle (\epsilon, q_1), (\epsilon, q_2), \ldots, (\epsilon, q_n) \rangle \mid q_1, \ldots, q_n \in Q \text{ and there is a path from } q \text{ to } q_n \text{ using only } \epsilon \text{ transitions}\}
\]</span>