  In this work, we propose a method to decompose signal temporal logic (STL)
tasks for multi-agent systems subject to constraints imposed by the
communication graph. Specifically, we propose to decompose tasks defined over
multiple agents which require multi-hop communication, by a set of sub-tasks
defined over the states of agents with 1-hop distance over the communication
graph. To this end, we parameterize the predicates of the tasks to be
decomposed as suitable hyper-rectangles. Then, we show that by solving a
constrained convex optimization, optimal parameters maximising the volume of
the predicate's super-level sets can be computed for the decomposed tasks. In
addition, we provide a formal definition of conflicting conjunctions of tasks
for the considered STL fragment and a formal procedure to exclude such
conjunctions from the solution set of possible decompositions. The proposed
approach is demonstrated through simulations.
