Input/Output Abstraction of State Based Systems

Abstraction of specifications is a method of making verification and validation of specifications and implementations more tractable. This paper considers the special case where the abstraction is defined by eliding input or output variables in state based specifications - in particular, conditions for such abstractions to be sound and complete with respect to a refinement semantics. Output abstractions turn out to be unconditionally sound, and combinations of output abstractions are complete in certain circumstances. Concrete results are developed in the state-based notation Z, and then considered in the underlying semantic framework and for similar languages.