Distributed Observation Problems∗

We introduce and study problems of distributed observation with bounded or unbounded memory. We are given a system modeled as a finite-word language L over some finite alphabet Σ and subalphabets Σ1, ...,Σn of Σ modeling n distinct observation points. We want to build (when there exist) n observers which collect projections of a behavior in L onto Σ1, ...,Σn, then send them to a central decision point. The latter must determine whether the original behavior was in a given K ⊆ L. In the unbounded-memory case, observers record the entire sequence they observe. In the bounded-memory case, they are required to be finite-