 weights of its transitions using an appropriate operation (e.g., multiplication for probabilities, addition for costs):</p>
<p><span class="math display">\[\text{weight}(p) = w_1 \otimes w_2 \otimes \ldots \otimes w_n\]</span></p>
<p>where <span class="math inline">\(\otimes\)</span> is the weight combination operation.</p>
<p>The weighted transduction algorithm returns the output string(s) with the optimal weight:</p>
<p><span class="math display">\[\text{best-transduce}(T, \boldsymbol\sigma) = \{\gamma \