"><a href="#cb1-25" aria-hidden="true" tabindex="-1"></a>We need a helper function to handle epsilon transitions. Let's define $\text{epsilon-paths}(q)$ as the set of all paths from state $q$ to any other state using only epsilon transitions:</span>
<span id="cb1-26"><a href="#cb1-26" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-27"><a href="#cb1-27" aria-hidden="true" tabindex="-1"></a>$$</span>
<span id="cb1-28"><a href="#cb1-28" aria-hidden="true" tabindex="-1"></a>\text{epsilon-paths}(q) =