d our parsing algorithm to collect the output symbols along each path. We'll define a function $\text{transduce}(T, \boldsymbol\sigma)$ that returns the set of all possible output strings if $\boldsymbol\sigma$ can be transduced by $T$, and the empty set otherwise.</span>
<span id="cb1-32"><a href="#cb1-32" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-33"><a href="#cb1-33" aria-hidden="true" tabindex="-1"></a>First, we need a helper function to handle epsilon transitions. Let's define $\text{e