Cross-Over Composition - Enforcement of Fairness under Unfair Adversary

We study a special type of self-stabilizing algorithms composition : the cross-over composition (A B). The cross-over composition is the generalization of the algorithm compiler idea introduced in [3]. The cross-over composition could be seen as a black box with two entries and one exit. The composition goal is to improve the qualities of the first algorithm A, using as medium the second algorithm B. Informally, the obtained algorithm is A after the transfer of B’s properties. Here, we provide a complete analysis of the composition, when the algorithms (A and B) are deterministic and/or probabilistic algorithms. Moreover, we show that the cross-over composition is a powerful tool in order to enforce a scheduler to have a fair behavior regarding to A.