On the Mailbox Problem

The Mailbox Problem was described and solved by Aguilera, Gafni, and Lamport in their 2010 DC paper with an algorithm that uses two flag registers that carry 14 values each. An interesting problem that they ask is whether there is a mailbox algorithm with smaller flag values. We give a positive answer by describing a mailbox algorithm with 6 and 4 values in the two flag registers.