ine">\(T\)</span>, and the empty set otherwise.</p>
<p>First, we need a helper function 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 input transitions:</p>
<p><span class="math display">\[\text{epsilon-paths}(q) = \{\langle (\epsilon, \gamma_1, q_1), (\epsilon, \gamma_2, q_2), \ldots, (\epsilon, \gamma_n, q_n) \rangle \mid q_1, \ldots, 