Double-spends

If a user tries to spend the same output twice, there are two possible situations:

1. There is partial order between the two units that try to spend the same output, i.e. one of the units (directly or indirectly) includes the other unit, and

   

   Figure 2

   therefore comes after it. In this case, it is obvious that we can safely reject the later unit.

2. There is no partial order between them. In this case, we accept both. We establish a total order between the units later on, when they are buried deep enough under newer units (see below how we do it). The one that appears earlier on the total order is deemed valid, while the other is deemed invalid

There is one more protocol rule that simplifies the definition of total order. We require, that if the same address posts more than one unit, it should include (directly or indirectly) all its previous units in every subsequent unit, i.e. there should be partial order between consecutive units from the same address. In other words, all units from the same author should be serial. If someone breaks this rule and posts two units such that there is no partial order between them (nonserial units), the two units are treated like double-spends even if they don’t try to spend the same output. Such nonserials are handled as described in situation 2 above.

Figure 2. Double-spends. There is no partial order between them. If a user follows this rule but still tries to spend the same output twice, the double-spends become unambiguously ordered and we can safely reject the later one as in situation 1 above. The double-spends that are not nonserials at the same time are hence easily filtered out. This rule is in fact quite natural. When a user composes a new unit, he selects the most recent other units as parents of his unit. By putting them on his parents list, he declares his picture of the world, which implies that he has seen these units. He has therefore seen all parents of parents, parents of parents of parents, etc up until the genesis unit. This huge set should obviously include everything that he himself has produced, and therefore has seen.

By not including a unit (even indirectly, through parents) the user denies that he has seen it. If we see that by not including his own previous unit a user denies having seen it, we’d say it’s odd, something fishy is going on. We discourage such behavior