  We compare the succinctness of two monitoring systems for properties of
infinite traces, namely parallel and regular monitors. Although a parallel
monitor can be turned into an equivalent regular monitor, the cost of this
transformation is a double-exponential blowup in the syntactic size of the
monitors, and a triple-exponential blowup when the goal is a deterministic
monitor. We show that these bounds are tight and that they also hold for
translations between corresponding fragments of Hennessy-Milner logic with
recursion over infinite traces.
