2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213987Lovasz and Schrijver, and later Lasserre, proposed hierarchies of semidefinite programming relaxations for general 0/1 linear programming problems. In this paper these two constructions are revisited and two new, block-diagonal hierarchies are proposed. They have the advantage of being computationally less costly while being at least as strong as the Lovasz-Schrijver hierarchy. Our construction is applied to the stable set problem and experimental results for Paley graphs are reported.11 pages, (v2) revision based on suggestions by referee, computation of N+(TH(P_q)) included in Table 2Optimization and Control90C22; 90C27text