 tuples, where each tuple represents a transition in the transducer. Formally, a path is represented as:</p>
<p><span class="math display">\[\langle (\sigma_1, \gamma_1, q_1), (\sigma_2, \gamma_2, q_2), \ldots, (\sigma_n, \gamma_n, q_n) \rangle\]</span></p>
<p>where <span class="math inline">\(q_i \in Q\)</span>, <span class="math inline">\(\sigma_i \in \Sigma \cup \{\epsilon\}\)</span>, <span class="math inline">\(\gamma_i \in \Gamma \cup \{\epsilon\}\)</span>, and <span class="math inline">\((q_i, \gamma_