\sigma = \epsilon \\
\text{transduce-from}(T, \sigma_2\ldots\sigma_n, P') &amp; \text{if } \boldsymbol\sigma = \sigma_1\sigma_2\ldots\sigma_n \\
\emptyset &amp; \text{otherwise}
\end{cases}\]</span></p>
<p>where: - <span class="math inline">\(\text{find-accepting-paths}(P)\)</span> returns the set of paths from <span class="math inline">\(P\)</span> that end in an accepting state, or <span class="math inline">\(\emptyset\)</span> if no such paths exist - <span class="math inline">\(\text{collect-outputs}(P)