  In this paper, we focus on the study of quotients of Boolean control networks
(BCNs) with the motivation that they might serve as smaller models that still
carry enough information about the original network. Given a BCN and an
equivalence relation on the state set, we consider a labeled transition system
that is generated by the BCN. The resulting quotient transition system then
naturally captures the quotient dynamics of the BCN concerned. We therefore
develop a method for constructing a Boolean system that behaves equivalently to
the resulting quotient transition system. The use of the obtained quotient
system for control design is discussed and we show that for BCNs, controller
synthesis can be done by first designing a controller for a quotient and
subsequently lifting it to the original model. We finally demonstrate the
applicability of the proposed techniques on a biological example.
