 consider all possible paths from the initial state via epsilon transitions:</p>
<p><span class="math display">\[\text{transduce}(T, \boldsymbol\sigma) = \text{transduce-from}(T, \boldsymbol\sigma, \{\langle \rangle \circ \epsilon\text{-path} \mid \epsilon\text{-path} \in \text{epsilon-paths}(q_0)\})\]</span></p>
<p>After reading the entire input string, we must also consider any epsilon transitions that can be taken from the final states:</p>
<p><span class="math display">\[\text{find-accepting-paths}(P) =