  We study cyclic binary strings with bounds on the lengths of the intervals of
consecutive ones and zeros. This is motivated by scheduling problems where such
binary strings can be used to represent the state (on/off) of a machine. In
this context the bounds correspond to minimum and maximum lengths of on- or
off-intervals, and cyclic strings can be used to model periodic schedules.
Extending results for non-cyclic strings is not straight forward. We present a
non-trivial tight compact extended network flow formulation, as well as valid
inequalities in the space of the state and start-up variables some of which are
shown to be facet-defining. Applying a result from disjunctive programming, we
also convert the extended network flow formulation into an extended formulation
over the space of the state and start-up variables.
