A Pseudo-Algorithmic Separation of Lines from Pseudo-Lines

S = fxij : i < jg be the set of the x-coordinates of the vertices i \ j of the collection. L induces a decomposition of the plane into regions bounded by edges and vertices. This decomposition, A(L), is called the arrangement of the pseudo-lines. It is known that pseudo-line arrangements have a richer combinatorial structure than arrangements of lines: the number of combinatorially di erent pseudo-line arrangements is much larger than the number of line arrangements, as shown by Goodman and Pollack [6].