We tackle a natural problem from distributed computing, involving time
-stamps. Let P = {p(1),p(2),...,p(N)} be a set of computing agents or
processes which synchronize with each other from time to time and exch
ange information about themselves and others. The gossip problem is th
e following: Whenever a set P subset of or equal to P meets, the proce
sses in P must decide amongst themselves which of them has the latest
information, direct or indirect, about each agent p in the system. We
propose an algorithm to solve this problem which is finite-state and l
ocal. Formally, this means that our algorithm can be implemented as an
asynchronous automaton.