Theorem 2.7

Theorem 2.7 (Loff–Moreira–Reis [7, Theorem 16, p. 21]). A language $L\subseteq\Sigma^*$ is in $\mathsf{PEG}$ if and only if its reversal $L^R$ is decided by some scaffolding automaton. In particular, if a finite scaffolding automaton decides $L$, then $L^R$ is recognized by a total complete-match PEG.