 \{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></p>
<p>Finally, to extract the output strings from a set of paths, we concatenate the output symbols along each path:</p>
<p><span class="math display">\[\text{collect-outputs}(P) = \{\gamma_1\gamma_2\ldots\gamma_n \mid \langle (\sigma_1, \gamma_1, q_1), (\sigma_2, \gamma_2, q_2), \ldots, (\sigma_n, \gamma_n, q_n) \rangle \in P\}\]</span>