  We study cutoff results for parameterized verification and synthesis of
guarded protocols, as introduced by Emerson and Kahlon (2000). Guarded
protocols describe systems of processes whose transitions are enabled or
disabled depending on the existence of other processes in certain local states.
Cutoff results reduce reasoning about systems with an arbitrary number of
processes to systems of a determined, fixed size. Our work is based on the
observation that existing cutoff results for guarded protocols are often
impractical, since they scale linearly in the number of local states of
processes in the system. We provide new cutoffs that scale not with the number
of local states, but with the number of guards in the system, which is in many
cases much smaller. Furthermore, we consider natural extensions of the classes
of systems and specifications under consideration, and present results for
problems that have not been known to admit cutoffs before.
