  In a recent work, Chen, Hoza, Lyu, Tal and Wu (FOCS 2023) showed an improved
error reduction framework for the derandomization of regular read-once
branching programs (ROBPs). Their result is based on a clever modification to
the inverse Laplacian perspective of space-bounded derandomization, which was
originally introduced by Ahmadinejad, Kelner, Murtagh, Peebles, Sidford and
Vadhan (FOCS 2020).
  In this work, we give an alternative error reduction framework for regular
ROBPs. Our new framework is based on a binary recursive formula from the work
of Chattopadhyay and Liao (CCC 2020), that they used to construct weighted
pseudorandom generators (WPRGs) for general ROBPs.
  Based on our new error reduction framework, we give alternative proofs to the
following results for regular ROBPs of length $n$ and width $w$, both of which
were proved in the work of Chen et al. using their error reduction:
  $\bullet$ There is a WPRG with error $\varepsilon$ that has seed length
$\tilde{O}(\log(n)(\sqrt{\log(1/\varepsilon)}+\log(w))+\log(1/\varepsilon)).$
  $\bullet$ There is a (non-black-box) deterministic algorithm which estimates
the expectation of any such program within error $\pm\varepsilon$ with space
complexity $\tilde{O}(\log(nw)\cdot\log\log(1/\varepsilon)).$ (This was first
proved in the work of Ahmadinejad et al., but the proof by Chen et al. is
simpler.)
  Because of the binary recursive nature of our new framework, both of our
proofs are based on a straightforward induction that is arguably simpler than
the Laplacian-based proof in the work of Chen et al.
