The problem of verifying the coherence of a probabilistic assignment on a finite set of conditional events has been recently examined by several authors ([6, 7, 10, 11, 25]). The algorithms proposed are substantially very similar and they all require to solve a sequence of systems of linear inequalities, such that the number of rows of each of these systems is determined by the solution found for the previous one. In the sequel, we shall
examine how the concept of strictly complementary solution of a linear program (LP) can be applied in this framework to reduce the number and the size of the systems to be solved.
