Hey,
if your cases are always like those in your illustrations,
problem is tractable without too much effort.
(for polygon sharing an arc, get list of arcs, deduplicate list, change
arcs into linestring, rebuild polygon using linestring).
If you want a solution in all generality (for instance
Hey ho everybody
We at sogis are looking for a way to convert arcs (curves) to lines without
producing slivers and overlaps of adjacent geometries sharing the same arc. It
is very important for us to find a postgis solution as postgis is the "working
horse" in all our automatic data