</p>
<p>Note that this set always includes the empty path <span class="math inline">\(\langle \rangle\)</span> from a state to itself via zero epsilon transitions.</p>
<p>We can now define a recursive parsing function <span class="math inline">\(\text{parse-from}_G(\boldsymbol\sigma, P)\)</span> where <span class="math inline">\(P\)</span> is a set of partial paths:</p>
<p><span class="math display">\[
\text{parse-from}_G(\boldsymbol\sigma, P) = \begin{cases}
\{p \in P \mid \text{last-state}(p) \in F\} &amp