  Translating continuous control system models into finite automata allows us
to use powerful discrete tools to synthesize controllers for complex
specifications. The abstraction construction step is unfortunately hamstrung by
high runtime and memory requirements for high dimensional systems. This paper
describes how the transition relation encoding the abstract system dynamics can
be generated by connecting smaller abstract modules in series and parallel. We
provide a composition operation and show that composing a collection of
abstract modules yields another abstraction satisfying a feedback refinement
relation. Through compositionality we circumvent the acute computational cost
of directly abstracting a high dimensional system and also modularize the
abstraction construction pipeline.
