Making an Agreement in an Order-Heterogeneous Group

Abstract

In traditional agreement protocols of multiple peer processes (peers), every peer just aims at agreeing on one value out of values shown by the peers. In meetings of human societies, agreement procedures are so flexible that persons can change their opinions and can use various types of agreement conditions. We already discuss E- and P-precedent relations v ₁ $\rightarrow_i^E$ v ₂ and v ₁ $\rightarrow_i^P$ v ₂ on values v ₁ and v ₂ of a peer p _i , which show that p _i can take v ₂ after taking v ₁ and prefers v ₁ to v ₂, respectively. If a peer autonomously takes values only based on its precedent relations, the peers might not make an agreement even if the values satisfy the agreement condition. We discuss what previous values the peer can take again an order-heterogenous system where some pair of peers have different precedent relations. In this paper, we discuss a cut, i.e. a satisfiable set of previous values in a history of values which the peers have so far taken, in addition for each peer to taking a new value at each round.