ting-paths}(P) = <span class="sc">\{</span>p \circ \epsilon\text{-path} \mid p \in P, \epsilon\text{-path} \in \text{epsilon-paths}(\text{last-state}(p)), \text{last-state}(\epsilon\text{-path}) \in F<span class="sc">\}</span>$$</span>
<span id="cb1-59"><a href="#cb1-59" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-60"><a href="#cb1-60" aria-hidden="true" tabindex="-1"></a>Finally, to extract the output strings from a set of paths, we concatenate the output symbols along each path:</span>
<spa