q_n \in Q \text{ and there is a path from } q \text{ to } q_n \text{ using only } \epsilon \text{ input transitions}\}\]</span></p>
<p>We’ll define a transduction function <span class="math inline">\(\text{transduce-from}(T, \boldsymbol\sigma, P)\)</span> where <span class="math inline">\(P\)</span> is a set of partial paths:</p>
<p><span class="math display">\[\text{transduce-from}(T, \boldsymbol\sigma, P) = \begin{cases}
\text{collect-outputs}(\text{find-accepting-paths}(P)) &amp; \text{if } \boldsymbol