Stability of long-lived consensus

This paper introdu es the notion of stability for a longlived onsensus system. This notion re e ts how sensitive to hanges the de isions of the system are, from one invoation of the onsensus algorithm to the next, with respe t to input hanges. Stable long-lived onsensus systems are proposed, and tight lower bounds on the a hievable stability are proved, for several di erent s enarios. The s enarios in lude systems that keep memory from one invo ation of onsensus to the next versus memoryless systems; systems that take their de isions based on the number of di erent inputs but not on the sour e identities of those inputs versus non-symmetri systems. These results intend to study essential aspe ts of stability, and hen e are independent of spe i models of distributed omputing. Appli ations to parti ular asyn hronous and syn hronous systems are des ribed.