This is intended to be a simpler version of my earlier question here.In this post, 1-Sokoban-search is Sokoban with only 1 box, 1-Sokoban-decision isthe corresponding decision problem, and 1-Sokoban refers to both of those problems.(You get to choose whether that also means there's only one storage location orstill allows more storage locations.  Everything I say here applies in either case.)1-Sokoban is trivially in NL.  Since, regardless of whether the ?s are X or blank, the region?  XXXXX?will have no box and no storage location and be such that the box can be pushedfrom the top to exit out the right but can't be pushed from the right to the top, (directed) Grid Graph Reachability / (directed) GG search   can easily be reduced to  1-Sokoban-decision / 1-Sokoban-search  respectively,so 1-Sokoban is NC1-hard and not known to be solvable by L.Grid Graph distance is known to be in  UL  coUL ,  so by any search-to-valuereduction, that is no obstacle to putting 1-Sokoban in  UL  coUL .(However, I don't have any evidence for 1-Sokoban being in even LpromiseFewL.)Is anything else known about 1-Sokoban?In particular, I have been unable to come up with any decision-to-search reduction in which the search oracle incorrectly reporting no solution never causes false negatives / search-to-decision reduction by any slightly-natural class, even with a GGsearch oracle, that can't obviously already solve all of  NL / FNL respectively, and I've also been unable to come up with anyevidence for or against hardness of 1-Sokoban, beyond the reduction from Grid Graphs.
Is anything known about Sokoban with only 1 box?
reductions;space bounded;nondeterminism